Virtual walks in the Ising model: Finite-time scaling

We use Pauli Path simulation to variationally obtain parametrized circuits for preparing ground states of various quantum many-body Hamiltonians. These include the quantum Ising model in one dimension, in two dimensions on square and heavy-hex lattices, and the Kitaev honeycomb model, all at system sizes of one hundred qubits or more – sizes at which generic quantum circuits are beyond the reach of exact state-vector simulation – thereby reaching utility scale. We benchmark the Pauli Path simulation results against exact ground-state energies when available, and against density-matrix renormalization group calculations otherwise, finding strong agreement. To further assess the quality of the variational states, we evaluate the magnetization in the x and z directions for the quantum Ising models and compute the topological entanglement entropy for the Kitaev honeycomb model. Finally, we prepare approximate ground states of the Kitaev honeycomb model with 48 qubits, in both the gapped and gapless regimes, on Quantinuum's System Model H2 quantum computer using parametrized circuits obtained from Pauli Path simulation. We achieve a relative energy error of approximately 5 % without error mitigation and demonstrate the braiding of Abelian anyons on the quantum device beyond fixed-point models.

Abstract The nature of diffusion is usually studied for particles or time-evolving systems. Similar in principle, such studies can be conducted by tracking how a given function of observable properties evolves over time-akin to the evolution of observable functions-referred to as functional-diffusion . This is not the same as the system’s individual trajectories, but can be regarded as a meta-trajectory. Following this idea, we measure how the approach to ergodicity evolves over time for the observed magnetization of a full Ising model with an external field. We compute the diffusive behavior of the functional across a range of temperatures via Metropolis and Glauber single-spin-flip dynamics. The system’s ensemble-averaged dynamics are computed using expressions from the exact solution. Power-law behavior in the approach to ergodicity provides a classification of anomalies in functional-diffusion , demonstrating nonlinear anomalous behavior over different temperature and field ranges. Studying the ergodicity convergence of these meta-trajectories can help validate and enhance the pedagogical understanding of nonequilibrium thermodynamic systems.

We introduce the , a nonperiodic analog of the discrete time crystal that arises in periodically driven dissipative quantum many-body systems. This phase is defined by two key features: (1) spatial long-range order arising from the spontaneous breaking of an internal symmetry and (2) temporally chaotic oscillations of the order parameter, whose lifetime diverges with system size. In other words, a time glass is a state of matter in which all components evolve in a synchronized yet chaotic manner. To characterize the time glass phase, we focus on the spectral gap of the one-cycle (Floquet) Liouvillian, which determines the decay rate of the slowest relaxation mode. Theoretical arguments and numerical studies of periodically driven dissipative Ising models show that, in the time glass phase, the Liouvillian gap remains finite in the thermodynamic limit, in contrast to time crystals where the gap closes exponentially with system size. We further demonstrate that the Liouvillian gap converges to the decay rate of the order-parameter autocorrelation derived from the classical (mean-field) dynamics in the thermodynamic limit. This result establishes a direct correspondence between microscopic spectral features and emergent macroscopic dynamics in driven dissipative quantum systems. At first glance, the existence of a nonzero Liouvillian gap appears incompatible with the presence of indefinitely persistent chaotic oscillations. We resolve this apparent paradox by showing that the quantum Rényi divergence between a localized coherent initial state and the highly delocalized steady state grows unboundedly with system size. This divergence allows long-lived transients to persist even in the presence of a finite Liouvillian gap.

Understanding the complex microbial interactions and their implications for host health is a critical endeavor in biomedical research. In this paper, we propose a transformation-free Bayesian inference approach for estimating microbial and metabolomic association networks based on a latent Ising model. Our method addresses the challenges posed by the compositionality and zero-inflation of microbiome data, offering computational efficiency and versatility for mixed data types. By integrating two-component mixture models tailored to microbiome and metabolome data, along with spike-and-slab priors for sparse graph estimation and a pseudolikelihood approximation for efficient Bayesian computation, we provide a unified framework for joint microbial and metabolomic network inference. Simulation studies demonstrate the superior performance of our method compared to existing approaches, and an application to a real bacterial vaginosis microbiome-metabolome dataset reveals intriguing interaction patterns. Our proposed approach offers a promising avenue for uncovering biological insights from complex microbiome data and holds potential for advancing our understanding of microbiome-associated diseases and therapeutic interventions.

Magnetic properties of a square core–shell nanowire with mixed spins (2,1/2) within the anisotropic Ising model: mean-field approach

Abstract Monte Carlo simulations using the Metropolis algorithm were carried out for the Heisenberg model, the two-state Ising model, and the 2 S + 1 state Ising model, focusing on ferromagnetic systems. The relationship between magnetic exchange interaction strength and the ferromagnetic transition temperature ( T C ) was evaluated and compared across the three models within the range of 1 / 2 ⩽ S ⩽ 10 . Additionally, the magnetocaloric properties, such as the isothermal magnetic entropy change ( Δ S mag ) and the relative cooling power, were assessed for two well-known ferromagnetic materials: Gd and EuS. Among the three models examined, the 2 S + 1 state Ising model demonstrated the best quantitative agreement with experimental results, whereas the Heisenberg model showed poor agreement.

Abstract Ideal gases adhere to the principles of the kinetic theory of gases. To illustrate their non-ideal characteristics, we derive the equation of state for the lattice gas model defined on a cubic lattice through mean-field theory (MFT). The central focus of this work is the introduction and application of hard-spin MFT (HS-MFT), which preserves the discrete nature of site occupancy (or equivalently, Ising spin variables) within a mean-field framework. The resulting equation of state contains a logarithmic term structurally similar to the Saha–Basu equation. While reproducing the standard mean-field result, HS-MFT yields a critical temperature significantly closer to Monte Carlo benchmarks and—crucially—correctly predicts the absence of a finite-temperature phase transition in one dimension, a well-known shortcoming of conventional mean-field treatments. We further analyze the critical point, critical exponents, law of corresponding states, Boyle temperature, Joule–Thomson coefficient, inversion temperature, and heat capacity relations derived from this equation of state. We believe that the progression from standard to HS-MFT offers students of statistical mechanics a richer, more physically consistent pathway to understanding phase transitions and non-ideal fluid behavior.

Triviality of the scaling limits of critical Ising and φ4 models with effective dimension at least four

The connectivity hypothesis, central to the increasingly influential symptom network approach to psychopathology, proposes that stronger connectivity among symptoms heightens vulnerability to mental disorders. We provide an analytic derivation of this hypothesis using mean-field Ising models of depression, both in the standard − 1 / 1 formulation and in a 0 / 1 variant where nodes represent symptoms as absent or present. Applying bifurcation theory, we derive the bifurcation sets and phase transition structure directly from the mean-field equations. This formal characterization elucidates how connectivity shapes system dynamics and, consistent with the network theory of mental disorders, demonstrates that increasing connectivity amplifies the risk of transitions into unhealthy states. • High connectivity in clinical network models drives transitions into unhealthy states. • The mean-field 0/1 Ising model exhibits an asymmetric cusp catastrophe. • We analytically derive bifurcation sets without series expansions.

The correlated cluster mean-field approach to the frustrated Ising model on the honeycomb lattice

Nonfactorizing interface in the two-dimensional long-range Ising model

We demonstrate that the stabilizer Rényi entropy (SRE), a computable measure of quantum magic, can serve as an information-theoretic probe for universal properties associated with conformal defects in one-dimensional quantum critical systems. Using boundary conformal field theory, we show that open boundaries manifest as a universal logarithmic correction to the SRE, whereas topological defects yield a universal size-independent term. When multiple defects are present, we find that the universal terms in the SRE faithfully reflect the defect-fusion rules that define a noninvertible symmtery algebra. These analytical predictions are corroborated by numerical calculations of the Ising model, where boundaries and topological defects are described by Cardy states and Verlinde lines, respectively.

Scarred ferromagnetic phase in the long-range transverse-field Ising model

In the present manuscript, we address and solve for the first time a nonlocal discrete isoperimetric problem. We consider indeed a generalization of the classical perimeter, what we call a nonlocal bi-axial discrete perimeter , where not only the external boundary of a polyomino \mathcal{P} contributes to the perimeter, but all internal and external components of \mathcal{P} . Furthermore, we find and characterize its minimizers in the class of polyominoes with fixed area n . Moreover, we explain how the solution of the nonlocal discrete isoperimetric problem is related to the rigorous study of the metastable behavior of a long-range bi-axial Ising model .

This article traces the 15-year journey (2010–2025) of pioneering research on van der Waals (vdW) magnets in Korea, starting from the original idea of “magnetic graphene”. I recount my early failures with oxide systems, and then the discovery of TMPS3 compounds as model 2D magnets in the early 2010s. Crucially, the first public talks were given in 2015–2016, including one at the 2015 Korean Physical Society Fall meeting, along with the publication of four papers in 2016. Notably, the FePS3 paper verified Onsager’s 2D Ising model experimentally, which established the foundation of the field. Our work and research done by other groups triggered a global interest in the field, making vdW magnetism a major topic in condensed matter and materials science worldwide. Finally, I end with my personal reflections on the future direction of the field.

Understanding the interplay between nonstabilizerness and entanglement is crucial for uncovering the fundamental origins of quantum complexity. Recent studies have proposed entanglement spectral quantities, such as antiflatness of the entanglement spectrum and entanglement capacity, as effective complexity measures, establishing direct connections to stabilizer Rényi entropies. In this work, we systematically investigate quantum complexity across a diverse range of spin models, analyzing how entanglement structure and nonstabilizerness serve as distinctive signatures of quantum phases. By studying entanglement spectra and stabilizer entropy measures, we demonstrate that these quantities consistently differentiate between distinct phases of matter. Specifically, we provide a detailed analysis of spin chains including the XXZ model, the transverse-field XY model, its extension with Dzyaloshinskii-Moriya interactions, as well as the Cluster Ising and Cluster XY models. Our findings reveal that entanglement spectral properties and magic-based measures serve as intertwined, robust indicators of quantum phase transitions, highlighting their significance in characterizing quantum complexity in many-body systems.

Abstract Periodically driven (Floquet) many-body systems tend to absorb energy and approach an infinite-temperature state, yet can host emergent order such as discrete time crystals (DTCs). Here we realise a clean two-dimensional DTC and an incommensurately modulated DTC (IM-DTC) on the IBM Quantum Heron processor, a 133-qubit superconducting device with heavy-hexagonal connectivity, implementing a kicked Ising model and tracking magnetisation dynamics for up to 100 Floquet cycles. We observe robust period-doubling oscillations that persist over the accessible time window and are stable against perturbations of the transverse field, without invoking disorder-induced many-body localisation or high-frequency Floquet prethermalisation. Introducing a longitudinal field generates additional long-period amplitude modulations with frequencies incommensurate with the drive, realising an IM-DTC response. Comparison with state-vector and tensor-network simulations benchmarks the hardware and reveals regimes where entanglement growth makes classical simulation challenging, underscoring the utility of gate-based quantum processors for out-of-equilibrium dynamics in two dimensions.

Generating large-scale Greenberger-Horne-Zeilinger–like states in lattice spin systems

Belief propagation (BP) is an efficient message-passing algorithm widely used for inference in graphical models and for solving various problems in statistical physics. However, BP often yields inaccurate estimates of order parameters and their susceptibilities in finite systems, particularly in sparse networks with few loops. Here, we show for both percolation and Ising models that fixing the state of a single well-connected “source” node to break global symmetry substantially improves inference accuracy and captures finite-size effects across a broad range of networks, especially treelike ones, at no additional computational cost.