Single Spin Flip Research Articles

Monte Carlo Simulations of the Spin-3/2 Ashkin-Teller Model in the Presence of Two Competing Dynamics

This paper studies, by means of Monte Carlo simulations, an open ferromagnetic spin-3/2 Ashkin-Teller model defined on a square lattice. This model can be viewed as the superposition of two Ising models which are coupled by a four-spin interaction strength K4while in each Ising model, the nearest-neighbor interaction constant is K2. The model is here submitted to two stochastic dynamics that consist of two processes; the first one is the Glauber dynamics which simulates the contact of the system with a heat bath at temperature T and the second one is the Kawasaki dynamics which simulates the continuous energy flux into the system from an external source. The Glauber single-spin flip process happens with the probability p while the Kawasaki spin-exchange process between neighboring sites occurs with the probability q = 1− p. The temperature-dependence of the system magnetizations for fixed coupling constants and lattice anisotropy has been thoroughly investigated. Several thermodynamic phases and phase transitions have been obtained as well as multicritical points. When the Kawasaki dynamics becomes dominant, self-organized antiferromagnetic phases are generated. Several phase diagrams have been devised to illustrate model thermodynamic properties.

SWAP algorithm for lattice spin models.

We adapted the SWAP molecular dynamics algorithm for use in lattice Ising spin models. We dressed the spins with a randomly distributed length and we alternated long-range spin exchanges with conventional single spin flip Monte Carlo updates, both accepted with a stochastic rule which respects detailed balance. We show that this algorithm, when applied to the bidimensional Edwards-Anderson model, speeds up significantly the relaxation at low temperatures and manages to find ground states with high efficiency and little computational cost. The exploration of spin models should help in understanding why SWAP accelerates the evolution of particle systems and sheds light on relations between dynamics and free-energy landscapes.

What will be the Euclidean dimension of an Ising ferromagnetic cubic shell?

The equilibrium and nonequilibrium properties of an Ising ferromagnetic cubic shell have been extensively studied by Monte Carlo simulation using Metropolis single spin flip algorithm. Although, geometrically the Euclidean dimension of the cubical shell is three, interestingly, the Ising ferromagnetic cubic shell undergoes ferromagnetic phase transition at a temperature which is very close to that for two-dimensional Ising ferromagnet. Surprisingly, the Ising ferromagnetic cubic shell shows a strange (neither exponential nor stretched exponential) kind of relaxation behaviour, instead of exponential relaxation as usually observed in the two dimensional Ising ferromagnet. The metastable lifetime of a ferromagnetic Ising cubical shell is studied as a function of the applied magnetic field. Here also, the cubic shell behaves more likely a two-dimensional object as found from statistical analysis and comparison with Becker–Döring prediction of classical nucleation theory.

Quenches in the Sherrington–Kirkpatrick model

The Sherrington–Kirkpatrick model is a prototype of a complex non-convex energy landscape. Dynamical processes evolving on such landscapes and locally aiming to reach minima are generally poorly understood. Here, we study quenches, i.e. dynamics that locally aim to decrease energy. We analyse the energy at convergence for two distinct algorithmic classes, single-spin flip and synchronous dynamics, focusing on greedy and reluctant strategies. We provide precise numerical analysis of the finite size effects and conclude that, perhaps counter-intuitively, the reluctant algorithm is compatible with converging to the ground state energy density, while the greedy strategy is not. Inspired by the single-spin reluctant and greedy algorithms, we investigate two synchronous time algorithms, the sync-greedy and sync-reluctant algorithms. These synchronous processes can be analysed using dynamical mean field theory (DMFT), and a new backtracking version of DMFT. Notably, this is the first time the backtracking DMFT is applied to study dynamical convergence properties in fully connected disordered models. The analysis suggests that the sync-greedy algorithm can also achieve energies compatible with the ground state, and that it undergoes a dynamical phase transition.

Nonequilibrium tricritical behavior in anisotropic XY ferromagnet driven by elliptically polarized propagating magnetic field wave

The three-dimensional anisotropic XY ferromagnet, driven by an elliptically polarized propagating magnetic field wave, has been extensively investigated by Monte Carlo simulation with the Metropolis single spin flip algorithm. Both the effects of the bilinear exchange type and the single-site anisotropies are thoroughly investigated. The time-averaged magnetization (over the complete cycle of the elliptically polarized propagating magnetic field wave) components play the role of the dynamic order parameter. For a fixed set of values of the strength of anisotropy and the field amplitudes, the system has been found to get dynamically ordered at a pseudocritical temperature. The pseudocritical temperature of such a dynamic nonequilibrium phase transition has been found to depend both on the strength of anisotropy and the amplitudes of the elliptically polarized propagating magnetic field wave. A comprehensive phase diagram is represented here in the form of an image plot of the pseudocritical temperature in the plane formed by the strength of anisotropy and field amplitudes. Interestingly, this nonequilibrium phase transition has been found to be discontinuous (first order) for higher values of the field amplitude. On the other hand, the continuous (second order) transition has been noticed for lower values of the field amplitude. Such an interesting nonequilibrium tricritical behavior has been observed in driven XY ferromagnet. The order of such a nonequilibrium phase transition has been confirmed by the thermal variation (near the transition) of the statistical distribution of the order parameter and by the thermal variation of the fourth-order Binder cumulant. In the plane formed by field amplitude and anisotropy, a tricritical line has been shown as the accompanying (and complementary) phase diagram. The dependence of the pseudocritical temperature, on the frequency and wavelength of the elliptically polarized propagating magnetic field wave, has also been reported.

Dynamical critical behavior of the two-dimensional three-state Potts model.

We investigate the dynamical critical behavior of the two-dimensional three-state Potts model with single spin-flip dynamics in equilibrium. We focus on the mean-squared deviation of the magnetization M (MSD_{M}) as a function of time, as well as on the autocorrelation function of M. Our simulations reveal the existence of two crossover behaviors at times τ_{1}∼L^{z_{1}} and τ_{2}∼L^{z_{2}}, separating three dynamical regimes. MSD_{M} appears to shift from ordinary diffusion in the first regime, to anomalous diffusion in the second, and finally to be constant in the third regime. The magnetization autocorrelation function, on the other hand, is found to fluctuate between exponential decay, stretched-exponential decay, and then again exponential decay along these three regimes. This behavior is in agreement with the one reported recently for the two-dimensional Ising ferromagnet [Phys. Rev. E 108, 034118 (2023)2470-004510.1103/PhysRevE.108.034118], indicating that the existence of two dynamic critical exponents is not a peculiarity of the Ising model itself. A comparison of both MSD_{M} and the magnetization's autocorrelation function suggests that within our numerical accuracy the exponents z_{1} and z_{2} are shared between the Ising and three-state Potts models at least for the particular case of single spin-flip dynamics studied here, even though their equilibrium universality classes are clearly distinct. Continuity of MSD_{M} requires that α(z_{2}-z_{1})=γ/ν-z_{1}, in which α is the anomalous exponent in the intermediate regime. Since the ratio γ/ν is not shared between the two models, it follows that α is not shared either, an aspect well verified in our simulations. Finally, we also discuss the relevance of our main findings using another useful observable, namely the line magnetization M_{l}.

Escaping fronts in local quenches of a confining spin chain

We consider local quenches from initial states generated by a single spin-flip in either the true or the false vacuum state of the confining quantum Ising spin chain in the ferromagnetic regime. Contrary to global quenches, where the light-cone behaviour is strongly suppressed, we find a significant light-cone signal propagating with a nonzero velocity besides the expected localised oscillating component. Combining an analytic representation of the initial state with a numerical description of the relevant excitations using the two-fermion approximation, we can construct the spectrum of post-quench excitations and their overlaps with the initial state, identifying the underlying mechanism. For confining quenches built upon the true vacuum, the propagating signal consists of superpositions of left and right-moving mesons escaping confinement. In contrast, for anti-confining quenches built upon the false vacuum it is composed of superpositions of left and right-moving bubbles which escape Wannier-Stark localisation.

Tuning the magnetic properties of doped ZnS using transition metal doping: A multi-scale computational approach

Transition metal (TM)-doped dilute magnetic semiconductors (DMS) have emerged as promising materials for spintronic applications such as spin-polarized transport and information storage. However, achieving robust room-temperature ferromagnetism in DMS remains a key challenge. This work undertakes a comprehensive investigation of the effects of Ti- and Cr-doping and (Ti,Cr)-codoping on the structural, electronic, and magnetic properties of wurtzite ZnS using first-principles pseudopotential plane-wave self-consistent field calculations and Monte Carlo simulations. The first-principles DFT calculations were performed using the spin-polarized GGA+U approach to account for strong electron–electron interactions. Structural relaxations revealed expanded lattice parameters and bond lengths for the doped systems compared to pure ZnS, attributed to the larger ionic radii of the dopants. Formation energy calculations confirmed the thermodynamic stability of doping. The band structure and density of states analysis demonstrated the half-metallic nature of the doped ZnS systems with 100% spin polarization induced by strong hybridization between the TM-3d and S-3p states. This mediates robust ferromagnetic coupling, with total magnetic moments around 4-8 μB/cell depending on dopant type and concentration. To complement the zero-temperature DFT results, temperature-dependent Monte Carlo simulations using the single-spin flip Heat Bath algorithm were implemented. The modeling of magnetization, susceptibility, specific heat, and hysteresis loops enabled extracting Curie temperatures up to 427.6 K for 12.5% Cr-doped ZnS. The synergistic combination of first-principles DFT and Monte Carlo computational techniques provides significant insights into tailoring the magnetic properties of TM-doped ZnS dilute magnetic semiconductors. The tunability of structural, electronic, and magnetic characteristics through control of dopant selection and concentration demonstrates the promising potential of transition metal-doped ZnS for spintronic devices operable at room-temperature.

Machine Learning of Nonequilibrium Phase Transition in an Ising Model on Square Lattice

This paper presents the investigation of convolutional neural network (CNN) prediction successfully recognizing the temperature of the nonequilibrium phase transitions in two-dimensional (2D) Ising spins on a square lattice. The model uses image snapshots of ferromagnetic 2D spin configurations as an input shape to provide the average output predictions. By considering supervised machine learning techniques, we perform Metropolis Monte Carlo (MC) simulations to generate the configurations. In the equilibrium Ising model, the Metropolis algorithm respects detailed balance condition (DBC), while its nonequilibrium version violates DBC. Violating the DBC of the algorithm is characterized by a parameter −8<ε<8. We find the exact result of the transition temperature Tc(ε) in terms of ε. If we set ε=0, the usual single spin-flip algorithm can be restored, and the equilibrium configurations generated with such a set up are used to train our model. For ε≠0, the system attains the nonequilibrium steady states (NESS), and the modified algorithm generates NESS configurations (test dataset). The trained model is successfully tested on the test dataset. Our result shows that CNN can determine Tc(ε≠0) for various ε values, consistent with the exact result.

Monte Carlo study of the phase transitions in the classical XY ferromagnets with random anisotropy

ABSTRACT The three-dimensional anisotropic classical XY ferromagnet has been investigated by extensive Monte Carlo simulation using the Metropolis single spin flip algorithm. The magnetisation (M) and the susceptibility (χ) are measured and studied as functions of the temperature of the system. For constant anisotropy, the ferro-para phase transition has been found to take place at a higher temperature than that observed in the isotropic case. The system gets ordered at higher temperatures for higher values of the strength of anisotropy. The opposite scenario is observed in the case of random anisotropy. For all three different kinds of statistical distributions (uniform, Gaussian, and bimodal) of random anisotropy, the system gets ordered at lower temperatures for higher values of the width of the distribution of anisotropy. We have provided the phase boundaries in the case of random anisotropy. The critical exponents for the scaling laws and are estimated through the finite size analysis.

Integrability and quench dynamics in the spin-1 central spin XX model

Central spin models provide an idealized description of interactions between a central degree of freedom and a mesoscopic environment of surrounding spins. We show that the family of models with a spin-1 at the center and XX interactions of arbitrary strength with surrounding spins is integrable. Specifically, we derive an extensive set of conserved quantities and obtain the exact eigenstates using the Bethe ansatz. As in the homogenous limit, the states divide into two exponentially large classes: bright states, in which the spin-1 is entangled with its surroundings, and dark states, in which it is not. On resonance, the bright states further break up into two classes depending on their weight on states with central spin polarization zero. These classes are probed in quench dynamics wherein they prevent the central spin from reaching thermal equilibrium. In the single spin-flip sector we explicitly construct the bright states and show that the central spin exhibits oscillatory dynamics as a consequence of the semilocalization of these eigenstates. We relate the integrability to the closely related class of integrable Richardson-Gaudin models, and conjecture that the spin-s central spin XX model is integrable for any s.

Accelerating equilibrium spin-glass simulations using quantum annealers via generative deep learning

Adiabatic quantum computers, such as the quantum annealers commercialized by D-Wave Systems Inc., are routinely used to tackle combinatorial optimization problems. In this article, we show how to exploit them to accelerate equilibrium Markov chain Monte Carlo simulations of computationally challenging spin-glass models at low but finite temperatures. This is achieved by training generative neural networks on data produced by a D-Wave quantum annealer, and then using them to generate smart proposals for the Metropolis-Hastings algorithm. In particular, we explore hybrid schemes by combining single spin-flip and neural proposals, as well as D-Wave and classical Monte Carlo training data. The hybrid algorithm outperforms the single spin-flip Metropolis-Hastings algorithm. It is competitive with parallel tempering in terms of correlation times, with the significant benefit of a much shorter equilibration time.

Liouvillian gap and single spin-flip dynamics in the dissipative Fermi-Hubbard model

Motivated by recent progress in cold-atom experiments, we analyze the SU($N$) Fermi-Hubbard model on a $d$-dimensional hypercubic lattice with two-body loss. By focusing on states near the ferromagnetic steady states, we obtain the Liouvillian gap in closed form for any $d$ and $N$. We also investigate the dynamics of a ferromagnetic initial state with a single spin flip both analytically and numerically. In particular, we show that, by decreasing the strength of the interaction and loss, the survival probability of the spin flip exhibits a crossover from the power-law decay to the exponential decay. We expect that our findings can be tested experimentally with ultracold alkaline-earth-like atoms in an optical lattice.

Parity Quantum Optimization: Encoding Constraints

Constraints make hard optimization problems even harder to solve on quantum devices because they are implemented with large energy penalties and additional qubit overhead. The parity mapping, which has been introduced as an alternative to the spin encoding, translates the problem to a representation using only parity variables that encodes products of spin variables. In combining exchange interaction and single spin flip terms in the parity representation, constraints on sums and products of arbitrary k-body terms can be implemented without additional overhead in two-dimensional quantum systems.

Canonical spin glass and cluster glass behavior in the polymorphs of LiFeSnO4

We report a comprehensive and comparative study of structural, static, dynamic, and nonequilibrium magnetic properties on the polymorphs of $\mathrm{LiFeSn}{\mathrm{O}}_{4}$. It exhibits two polymorphs: (i) orthorhombic phase (HT) stabilized at high temperature and (ii) hexagonal phase (LT) obtained at lower synthetic temperature. The HT phase crystallizes in the orthorhombic structure (space group: Pmcn) and exhibits a site disordered, nonfrustrated zig-zag network of ${\mathrm{Fe}}^{3+}$ and ${\mathrm{Sn}}^{4+}$ ions. On the other hand, the LT phase shows a disordered frustrated kagome network of ${\mathrm{Li}}^{1+}, {\mathrm{Fe}}^{3+}$, and ${\mathrm{Sn}}^{4+}$ ions crystallizing in the hexagonal structure (space group: $P{6}_{3}mc$). The low-temperature thermo-magnetic irreversibility and the absence of heat capacity anomaly in both polymorphs indicate the absence of long-range magnetic ordering and a possible glassy state. Zero-field-cooled and field-cooled magnetic memory effect and spin relaxation measurements stipulate the spin glass nature of the polymorphs. Further, spin glass behavior is confirmed by the AC susceptibility measurements. Interestingly, these polymorphs reveal different classes of spin glass states. The site disordered HT phase exhibits a single spin-flip time ${\ensuremath{\tau}}_{0}\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ sec, indicating a canonical spin glass state. In contrast, LT phase, which is disordered and geometrically frustrated, shows the spin-flip time of ${\ensuremath{\tau}}_{0}\ensuremath{\sim}9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ sec, suggesting a cluster spin glass state. In addition, the exchange bias effect was observed due to magnetic inhomogeneity in both polymorphs.

Time-dependent exchange creates the time-frustrated state of matter

Magnetic systems governed by exchange interactions between magnetic moments harbor frustration that leads to ground state degeneracy and results in the new topological state often referred to as a frustrated state of matter (FSM). The frustration in the commonly discussed magnetic systems has a spatial origin. Here we demonstrate that an array of nanomagnets coupled by the real retarded exchange interactions develops a new state of matter, time frustrated matter (TFM). In a spin system with the time-dependent retarded exchange interaction, a single spin-flip influences other spins not instantly but after some delay. This implies that the sign of the exchange interaction changes, leading to either ferro- or antiferromagnetic interaction, depends on time. As a result, the system’s temporal evolution is essentially non-Markovian. The emerging competition between different magnetic orders leads to a new kind of time-core frustration. To establish this paradigmatic shift, we focus on the exemplary system, a granular multiferroic, where the exchange transferring medium has a pronounced frequency dispersion and hence develops the TFM.

(Dis)assortative partitions on random regular graphs

We study the problem of assortative and disassortative partitions on random d-regular graphs. Nodes in the graph are partitioned into two non-empty groups. In the assortative partition every node requires at least H of their neighbors to be in their own group. In the disassortative partition they require less than H neighbors to be in their own group. Using the cavity method based on analysis of the belief propagation algorithm we establish for which combinations of parameters (d, H) these partitions exist with high probability and for which they do not. For we establish that the structure of solutions to the assortative partition problems corresponds to the so-called frozen-one-step replica symmetry breaking. This entails a conjecture of algorithmic hardness of finding these partitions efficiently. For we argue that the assortative partition problem is algorithmically easy on average for all d. Further we provide arguments about asymptotic equivalence between the assortative partition problem and the disassortative one, going through a close relation to the problem of single-spin-flip-stable states in spin glasses. In the context of spin glasses, our results on algorithmic hardness imply a conjecture that gapped single spin flip stable states are hard to find which may be a universal reason behind the observation that physical dynamics in glassy systems display convergence to marginal stability.

Monte Carlo study of the phase diagram of layered XY antiferromagnet

The three-dimensional XY model is investigated in the presence of a uniform magnetic field applied in the X-direction. The nearest neighbour intraplanar interaction is considered ferromagnetic, and the interplanar nearest neighbour interaction is chosen to be antiferromagnetic. Starting from a high-temperature initial random spin configuration, the equilibrium phase of the system at any finite temperature was achieved by cooling the system using the Monte Carlo single spin-flip Metropolis algorithm with a random updating rule. The components of total magnetization and the sublattice magnetizations were calculated. The variance of the antiferromagnetic order parameter and the susceptibility have been calculated. In a specific range of relative strengths of interactions (antiferromagnetic/ferromagnetic) and the applied magnetic field, the system shows the equilibrium phase transitions at different temperatures. The phase diagrams (in the field-temperature plane) were obtained for different values of the relative interaction strengths. The ordered region bounded by the phase boundary was found to increase as the ratio of relative interaction strength increased. Furthermore, the maximum value of the susceptibility (χaym) was found to increase with the system size (L). For χaym∼Lγν, the exponent γ/ν has been estimated to be 2.10 ±0.11.

Coulomb phase corrections to the transverse analyzing power AN(t) in high-energy forward proton-proton scattering

Study of polarized proton-proton elastic scattering in the Coulomb-nuclear interference region allows one to measure the forward hadronic single spin-flip amplitude including its phase. However, in a precision experimental data analysis, a phase-shift correction ${\ensuremath{\delta}}_{C}$ due to the long distance Coulomb interaction should be taken into account. For unpolarized scattering, ${\ensuremath{\delta}}_{C}$ is commonly considered as well established. Here, we evaluate the Coulomb phase shifts for the forward elastic proton-proton single spin-flip electromagnetic and hadronic amplitudes. Only a small discrepancy between the spin-flip and nonflip phases was found which can be neglected in the high-energy forward elastic $pp$ studies involving transverse spin. Nonetheless, the effective alteration of the hadronic spin-flip amplitude by the long-distance electromagnetic corrections can be essential for interpretation of the experimental results.

Nematicity and fractional magnetization plateaus induced by spin-lattice coupling in the classical kagome-lattice Heisenberg antiferromagnet

We investigate the effect of spin-lattice coupling (SLC) on the magnetic properties of the classical kagome-lattice Heisenberg antiferromagnet (KHAF) using improved Monte Carlo updates. The lattice modes are represented by Einstein site phonons, which introduce effective further-neighbor spin interactions in addition to the nearest-neighbor biquadratic interactions. In the weak SLC, the macroscopically degenerate coplanar ground state remains at zero field, while a $\sqrt{3} \times \sqrt{3}$ ordered phase accompanied by a 1/3-magnetization plateau appears in external magnetic fields. In the strong SLC, we find a nematic order at zero field and a 1/9-magnetization plateau associated with a $3 \times 3$ collinear order. Near the phase transition between the 1/9- and 1/3-plateau states, the ergodicity in the single spin flip is practically broken, and slow dynamics appear. We propose that relevant KHAFs with strong SLC would be realized in spinel-based materials.