Exact Thermodynamics Research Articles

New exact solutions, thermodynamics and phase transition in the Einstein–Maxwell-dilaton theory

New exact solutions, thermodynamics and phase transition in the Einstein–Maxwell-dilaton theory

Exact thermodynamics and transport in the classical sine-Gordon model

We revisit the exact thermodynamic description of the classical sine-Gordon field theory, a well-known integrable model. We found that existing results in the literature based on the soliton-gas picture did not correctly take into account light, but extended, solitons and thus led to incorrect results. This issue is regularized upon requantization: we derive the correct thermodynamics by taking the semiclassical limit of the quantum model. Our results are then extended to transport settings by means of Generalized Hydrodynamics.

More exact thermodynamics of nonlinear charged AdS black holes in 4D critical gravity

In this paper, we investigate nonlinearly charged AdS black holes in four-dimensional critical gravity and study more exact black hole thermodynamics under the effect of small statistical fluctuations. We compute the correction to the thermodynamics of nonlinearly charged AdS black hole up to the leading order. We discuss the stability of black holes under the circumstances of fluctuation and find that fluctuation causes instability in the black holes. Moreover, both the isothermal and adiabatic compressibilities are also derived. Finally, we estimate the role of small fluctuations on the equation of states and study the P−v diagram of nonlinearly charged AdS black hole.

Exact nonsingular black holes and thermodynamics

We show that regular black holes given by Culetu [14] can be obtained by coupling Einstein's gravity with the nonlinear electrodynamics source. The non-singular black hole has a mass function m(r)=Me−k/r, k is the deviation parameter, and it interpolates between the Schwarzschild black hole (k=0) and the Reissner-Nordstrom black hole (r≫k). Interestingly, there exists a critical mass parameter M=Mc, which corresponds to an extremal black hole when Cauchy and event horizons coincide. For M>Mc, it describes a nonextremal black hole with two horizons and no black hole for M<Mc. The Hawking temperature of the nonsingular black hole is maximum, where the specific heat diverges and changes its sign at the value of mass Mc2>Mc1, and the second-order phase transition occurs at that point. The smaller nonsingular black holes are always stable due to positive heat capacity and negative free energy. A discussion on the quasinormal modes of scalar field perturbations on nonsingular black holes background is included.

Integrable spin chain with Hilbert space fragmentation and solvable real-time dynamics.

We revisit the so-called folded XXZ model, which was treated earlier by two independent research groups. We argue that this spin-1/2 chain is one of the simplest quantum integrable models, yet it has quite remarkable physical properties. The particles have constant scattering lengths, which leads to a simple treatment of the exact spectrum and the dynamics of the system. The Hilbert space of the model is fragmented, leading to exponentially large degeneracies in the spectrum, such that the exponent depends on the particle content of a given state. We provide an alternative derivation of the Hamiltonian and the conserved charges of the model, including an alternative interpretation of the so-called "dual model" considered earlier. We also construct a nonlocal map that connects the model with the Maassarani-Mathieu spin chain, also known as the SU(3) XX model. We consider the exact solution of the model with periodic and open boundary conditions, and also derive multiple descriptions of the exact thermodynamics of the model. We consider quantum quenches of different types. In one class of problems the dynamics can be treated relatively easily: we compute an example for the real-time dependence of a local observable. In another class of quenches the degeneracies of the model lead to the breakdown of equilibration, and we argue that they can lead to persistent oscillations. We also discuss connections with the TT[over ¯] and hard rod deformations known from quantum field theories.

Low-temperature thermodynamics of the antiferromagnetic J1−J2 model: Entropy, critical points, and spin gap

The antiferromagnetic $J_1-J_2$ model is a spin-1/2 chain with isotropic exchange $J_1 > 0$ between first neighbors and $J_2 = \alpha J_1$ between second neighbors. The model supports both gapless quantum phases with nondegenerate ground states and gapped phases with $\Delta(\alpha) > 0$ and doubly degenerate ground states. Exact thermodynamics is limited to $\alpha = 0$, the linear Heisenberg antiferromagnet (HAF). Exact diagonalization of small systems at frustration $\alpha$ followed by density matrix renormalization group (DMRG) calculations returns the entropy density $S(T,\alpha,N)$ and magnetic susceptibility $\chi(T,\alpha,N)$ of progressively larger systems up to $N = 96$ or 152 spins. Convergence to the thermodynamics limit, $S(T,\alpha)$ or $\chi(T,\alpha)$, is demonstrated down to $T/J \sim 0.01$ in the sectors $\alpha < 1$ and $\alpha > 1$. $S(T,\alpha)$ yields the critical points between gapless phases with $S^\prime(0,\alpha) > 0$ and gapped phases with $S^\prime(0,\alpha) = 0$. The $S^\prime(T,\alpha)$ maximum at $T^*(\alpha)$ is obtained directly in chains with large $\Delta(\alpha)$ and by extrapolation for small gaps. A phenomenological approximation for $S(T,\alpha)$ down to $T = 0$ indicates power-law deviations $T^{-\gamma(\alpha)}$ from $\exp(-\Delta(\alpha)/T)$ with exponent $\gamma(\alpha)$ that increases with $\alpha$. The $\chi(T,\alpha)$ analysis also yields power-law deviations, but with exponent $\eta(\alpha)$ that decreases with $\alpha$. $S(T,\alpha)$ and the spin density $\rho(T,\alpha) = 4T\chi(T,\alpha)$ probe the thermal and magnetic fluctuations, respectively, of strongly correlated spin states. Gapless chains have constant $S(T,\alpha)/\rho(T,\alpha)$ for $T < 0.10$. Remarkably, the ratio decreases (increases) with $T$ in chains with large (small) $\Delta(\alpha)$.

Exact thermodynamics and phase diagram of integrable t-J model with chiral interaction

We study the phase diagram and finite temperature properties of an integrable generalization of the one-dimensional super-symmetric t-J model containing interactions explicitly breaking parity-time reversal (PT) symmetries. To this purpose, we apply the quantum transfer matrix method which results in a finite set of non-linear integral equations. We obtain numerical solutions to these equations leading to results for thermodynamic quantities as a function of temperature, magnetic field, particle density and staggering parameter. Studying the maxima lines of entropy at low but non zero temperature reveals the phase diagram of the model. There are ten different phases which we may classify in terms of the qualitative behaviour of auxiliary functions, closely related to the dressed energy functions.

Comparison of the exact thermodynamics of the AF Blume–Emery–Grifiths and of the spin-1 ferromagnetic Ising models

We study in detail the thermodynamics of the anti-ferromagnetic Blume–Emery–Griffiths (AF BEG) model in the presence of a longitudinal magnetic field. Its thermodynamics is derived from the exact Helmholtz free energy (HFE) of the model, valid for T>0. Numerical simulations of this model on a periodic space chain with 10 sites (N=10) yield the energy spectra of the model at KJ=2 for DJ=1 and DJ=2, thus helping us compare, for a broad range of temperature, how some (per site) thermodynamic functions with the same value of KJ but distinct values of DJ behave, namely: the z-component of the magnetization, the specific heat and the entropy. These thermodynamic functions of the AF BEG model at K|J|=2 are compared to those of the spin-1 ferromagnetic Ising model with D|J|>1.5, for which the T=0 phase diagrams of both models are identical. This comparison is done in a large interval of temperature.

Exact solution and thermodynamics of a spin chain with long-range elliptic interactions

We solve in closed form the simplest (su(1|1)) supersymmetric version of Inozemtsev's elliptic spin chain, as well as its infinite (hyperbolic) counterpart. The solution relies on the equivalence of these models to a system of free spinless fermions and on the exact computation of the Fourier transform of the resulting elliptic hopping amplitude. We also compute the thermodynamic functions of the finite (elliptic) chain and their low temperature limit and show that the energy levels become normally distributed in the thermodynamic limit. Our results indicate that at low temperatures the su(1|1) elliptic chain behaves as a critical XX model and deviates in an essential way from the Haldane–Shastry chain.

Adsorption preference reversal phenomenon from multisite-occupancy theory for two-dimensional lattices

The statistical thermodynamics of polyatomic species mixtures adsorbed on two-dimensional substrates was developed on a generalization in the spirit of the lattice-gas model and the classical Guggenheim-DiMarzio approximation. In this scheme, the coverage and temperature dependence of the Helmholtz free energy and chemical potential are given. The formalism leads to the exact statistical thermodynamics of binary mixtures adsorbed in one dimension, provides a close approximation for two-dimensional systems accounting multisite occupancy and allows to discuss the dimensionality and lattice structure effects on the known phenomenon of adsorption preference reversal.

Scaling Theory vs Exact Numerical Results for Spinless Resonant Level Model

The continuous-time quantum Monte Carlo method is applied to the interacting resonant level model (IRLM) using double expansion with respect to Coulomb interaction Ufc and hybridization V. Thermodynamics of the IRLM without spin is equivalent to the anisotropic Kondo model in the low-energy limit. Exact dynamics and thermodynamics of the IRLM are derived numerically for a wide range of Ufc with a given value of V. For negative Ufc, excellent agreement including a quantum critical point is found with a simple scaling formula that deals with V in the lowest-order, and Ufc up to infinite order. As Ufc becomes positive and large, lower order scaling results deviate from exact numerical results. Possible relevance of the results is discussed to certain Samarium compounds with unusual heavy-fermion behavior.

The magnetization plateaus of the ferro and anti-ferro spin-1 classical models with Sz2 term

We study in detail the exact thermodynamics of the one-dimensional standard and staggered spin-1 Ising models with a single-ion anisotropy term in the presence of a longitudinal magnetic field at low temperatures. The results are valid for the ferromagnetic and anti-ferromagnetic (AF) models and for positive and negative values of the crystal field for T>0. Although the excited states of the ferro and anti-ferro models are highly degenerate, we show that the temperature required for reaching the first excited state in the classical spin-1 ferro model gives a scale of temperature that permits fitting the z-component of the magnetization only by the contribution of two ground states of the model. This approximation is not true for the equivalent AF function due to the fact that the AF model is gapless along the lines separating the phases in its phase diagram at T=0. We relate the number of plateaus in the magnetization of each model to their respective phase diagrams at T=0. The specific heat per site of the AF model distinguishes, at low temperature, the transitions A⇌E and G⇌E as the external magnetic field is varied. The exact Helmholtz free energy of the classical spin-1 model is mapped onto the equivalent function of the ionic limit of the 1D extended Hubbard model by proper transformations.

Thermodynamics of Two-Component Log-Gases with Alternating Charges

We consider a one-dimensional gas of positive and negative unit charges interacting via a logarithmic potential, which is in thermal equilibrium at the (dimensionless) inverse temperature $\beta$. In a previous paper [Samaj, L.: J. Stat. Phys. 105, 173-191 (2001)], the exact thermodynamics of the unrestricted log-gas of pointlike charges was obtained using an equivalence with a (1+1)-dimensional boundary sine-Gordon model. The present aim is to extend the exact study of the thermodynamics to the log-gas on a line with alternating $\pm$ charges. The formula for the ordered grand partition function is obtained by using the exact results of the Thermodynamic Bethe ansatz. The complete thermodynamics of the ordered log-gas with pointlike charges is checked by a small-$\beta$ expansion and at the collapse point $\beta_c=1$. The inclusion of a small hard core around particles permits us to go beyond the collapse point. The differences between the unconstrained and ordered versions of the log-gas are pointed out.

Statistical thermodynamics of molecules with multiple adsorption states: Application to protein adsorption

The statistical thermodynamics of molecules with multiple adsorption states has been studied using a lattice model. The thermodynamic functions, calculated for a system characterized by two adsorption states, were applied to describe the adsorption of antifreeze proteins onto an ice crystal. The theoretical formalism reproduces the classical Langmuir equation (one-state limit), leads to the exact statistical thermodynamics of molecules adsorbed in one dimension with n different adsorption states, and seems to be a promising way toward a more accurate description of the adsorption thermodynamics of structurally diverse proteins.

Thermodynamics, spin-charge separation, and correlation functions of spin-1/2fermions with repulsive interaction

We investigate the low temperature thermodynamics and correlation functions of one-dimensional spin-1/2 fermions with strong repulsion in an external magnetic field via the thermodynamic Bethe ansatz method. The exact thermodynamics of the model in a weak magnetic field is derived with the help of Wiener-Hopf techniques. It turns out that the low energy physics can be described by spin-charge separated conformal field theories of an effective Tomonaga-Luttinger liquid and an antiferromagnetic SU(2) Heisenberg spin chain. However, these two types of conformally invariant low-lying excitations may break down as excitations take place far away from the Fermi points. The long distance asymptotics of the correlation functions and the critical exponents for the model in the presence of a magnetic field at zero temperature are derived in detail by solving dressed charge equations and by conformal mapping. Furthermore, we calculate the conformal dimensions for particular cases of correlation functions. The leading terms of these correlation functions are given explicitly for a weak magnetic field $H\ll 1$ and for a magnetic field close to the critical field $H\rightarrow H_{c}$. Our analytical results provide insights into universal thermodynamics and criticality in one-dimensional many-body physics.

Statistical thermodynamics of straight rigid rods with nonadditive lateral interactions: Theory and Monte Carlo simulations

The statistical thermodynamics of straight rigid rods of length k (k-mers) with nonadditive lateral interactions was developed on a generalization in the spirit of the lattice-gas model and the classical Bragg-Williams approximation (BWA) and the quasichemical approximation (QCA). The new theoretical framework is obtained by combining (i) the exact analytical expression for the partition function of noninteracting linear k-mers adsorbed in one dimension and its extension to higher dimensions, and (ii) a generalization of BWA and QCA in which the adsorbate can occupy more than one adsorption site. The traditional assumption of a strictly pairwise additive nearest-neighbors interaction is replaced by a more general one, namely that the bond linking a certain atom with any of its neighbors depends considerably on how many of them are actually present (or absent) on the sites in the first coordination shell of the atom. The coverage and temperature dependence of the Helmholtz free energy, chemical potential, configurational entropy, and differential heat of adsorption are given. The formalism (i) reproduces the classical results for monomers, (ii) leads to the exact statistical thermodynamics of nonadditive interacting k-mers adsorbed in one dimension, and (iii) provides a close approximation for two-dimensional systems, taking into account multisite occupancy and nonadditive lateral interactions. Comparisons with Monte Carlo simulations are performed in order to test the validity of the theoretical model. Significant quantitative differences are shown and discussed. In all cases, the QCA appears to be the more accurate approach.

Introduction to Integrable Many-Body systems III

Introduction to Integrable Many-Body systems IIIThis is the third part of a three-volume introductory course about integrable systems of interacting bodies. The emphasis is put onto the method of Thermodynamic Bethe ansatz. Two kinds of integrable models are studied. Systems of itinerant electrons, forming a part of Condensed Matter Physics, involve the Hubbard lattice model of electrons with short-ranged one-site interactions (Sect. 20) and the s-d exchange Kondo model (Sect. 21), describing the scattering of conduction electrons on a spin-s impurity. Methods and basic concepts used in Quantum Field Theory are explained on the integrable (1 + 1)-dimensional sine-Gordon model. We start with the classical description of the model in Sect. 22, analyze its finite energy field configurations (soliton, anti-soliton and breathers) and show its classical integrability. The model is quantized by using two schemes: the conformal (Sect. 23) and Lagrangian (Sect. 24) quantizations. The scattering matrix of the sine-Gordon theory is derived at the full quantum level in the bootstrap scheme and is compared to its classical limit in Sect. 25. The parameters of the scattering matrix are related to those of the Lagrangian by calculating the ground-state energy in an applied magnetic field in two ways: Conformal perturbation theory and Thermodynamic Bethe ansatz (Sect. 26). The relation of the sine-Gordon theory to the XXZ Heisenberg model, which provides a complete solution of the sine-Gordon model in a finite volume, is pointed out in Sect. 27. The obtained results are applied in Sect. 28. to the derivation of the exact thermodynamics for the (symmetric) two-component Coulomb gas; this is the first classical two-dimensional fluid with exactly solvable thermodynamics.

Universal Tomonaga-Luttinger liquid phases in one-dimensional strongly attractive SU(N)fermionic cold atoms

A simple set of algebraic equations is derived for the exact low-temperature thermodynamics of one-dimensional multicomponent strongly attractive fermionic atoms with enlarged SU$(N)$ spin symmetry and Zeeman splitting. Universal multicomponent Tomonaga-Luttinger liquid (TLL) phases are thus determined. For linear Zeeman splitting, the physics of the gapless phase at low temperatures belongs to the universality class of a two-component asymmetric TLL corresponding to spin-neutral $N$-atom composites and spin-$(N\ensuremath{-}1)/2$ single atoms. The equation of state which we obtained provides a precise description of multicomponent composite fermions and opens up the study of quantum criticality in one-dimensional systems of $N$-component Fermi gases with population imbalance.

Vector unparticle enhanced black holes: Exact solutions and thermodynamics

Tensor and scalar unparticle couplings to matter have been shown to enhance gravitational interactions and provide corrections to the Schwarzschild metric and associated black hole structure. We derive an exact solution to the Einstein equations for vector unparticles, and conclusively demonstrate that these induce Riessner–Nordström (RN)-like solutions where the role of the “charge” is defined by a composite of unparticle phase space parameters. These black holes admit double-horizon structure, although unlike the RN metric these solutions have a minimum inner horizon value. In the extremal limit, the Hawking temperature is shown to vanish. As with the scalar/tensor case, the (outer) horizon is shown via entropy considerations to behave like a fractal surface of spectral dimension dH=2dU.

Exact statistical thermodynamics of alkane binary mixtures in zeolites: New interpretation of the adsorption preference reversal phenomenon from multisite-occupancy theory

The rigorous statistical thermodynamics of mixtures of polyatomic species adsorbed on one-dimensional substrates is presented. The thermodynamic functions calculated for a monomer–dimer mixture are applied to describe the adsorption of methane–ethane mixtures in zeolites. The theoretical formalism reproduces the main features of the system, showing that the displacement of ethane by methane at higher pressures, a phenomenon known as Adsorption Preference Reversal, is the result of the difference of size (or number of occupied sites) between the adsorbed species.