Bulk diffusion in the undamped Frenkel-Kontorova model

We present new simulation results for the undamped Frenkel-Kontorova model. These support the existence of the bulk diffusion coefficient D, which has been called into question by earlier simulation work of Schneider and Stoll. We point out that D can be studied by three independent routes, and we show that these all provide evidence for the existence of D and yield the same numerical value for it in the particular thermodynamic state examined.     

Product Vacua with Boundary States and the Classification of Gapped Phases

We address the question of the classification of gapped ground states in one dimension that cannot be distinguished by a local order parameter. We introduce a family of quantum spin systems on the one-dimensional chain that have a unique gapped ground state in the thermodynamic limit that is a simple product state, but which on the left and right half-infinite chains have additional zero energy edge states. The models, which we call Product Vacua with Boundary States, form phases that depend only on two integers corresponding to the number of edge states at each boundary. They can serve as representatives of equivalence classes of such gapped ground states phases and we show how the AKLT model and its SO(2J + 1)-invariant generalizations fit into this classification.     

Thermodynamic model of the stabilization of an intermediate state in the region of the metamagnetic phase transition in erbium orthoferrite

The possible mechanisms of the thermodynamic stabilization of an intermediate state in the first-order metamagnetic phase transition in a magnetic field parallel to the Ising c axis of the Er³⁺ ions in erbium orthoferrite at T = 1.6 K have been analyzed. The model is chosen using the magneto-optical experimental data on the features of this state.     

Study of the 1D anisotropic Kondo necklace model at criticality via an entanglement entropy estimator

We use an estimator of quantum criticality based on the entanglement entropy to discuss the ground state properties of the 1D anisotropic Kondo necklace model. We found that the T=0$T=0$ phase diagram of the model is described by a critical line separating an antiferromagnetic phase from a Kondo singlet state. Moreover we calculate the conformal anomaly on the critical line and obtain that c tends to 0.5 as the thermodynamic limit is reached. Hence we conclude that these transitions belong to Ising universality class being, therefore, second order transitions instead of infinite order as claimed before.     

Time's arrow in an oscillating universe

In view of the time-symmetric nature of the laws of physics, time asymmetry in the universe must arise from “initial” conditions. A fully time-symmetric oscillating model is presented which exists in a highly compressed, highly ordered state att=0 and evolves forward, in the thermodynamic sense, as ∣t ∣ increases. This model offers the possibility of accounting for several fundamental and puzzling aspects of our universe, including matter-antimatter asymmetry, the large entropy per baryon, primordial density enhancements sufficient to form galaxies, and large-scale homogeneity.     

The density of states for an antiferromagnetic Ising model on a triangular lattice

The Wang-Landau algorithm is an efficient Monte Carlo approach to the density of states of a statistical mechanics system. The estimation of state density would allow the computation of thermodynamic properties of the system over the whole temperature range. We apply this sampling method to study the phase transitions in a triangular Ising model. The entropy of the lattice at zero temperature as well as other thermodynamic properties is computed. The calculated thermodynamic properties are explained in the context of the magnetic phase transition.      

A Hamilton-Jacobi formalism for thermodynamics

We show that classical thermodynamics has a formulation in terms of Hamilton-Jacobi theory, analogous to mechanics. Even though the thermodynamic variables come in conjugate pairs such as pressure/volume or temperature/entropy, the phase space is odd-dimensional. For a system with n thermodynamic degrees of freedom it is 2n+1-dimensional. The equations of state of a substance pick out an n-dimensional submanifold. A family of substances whose equations of state depend on n parameters define a hypersurface of co-dimension one. This can be described by the vanishing of a function which plays the role of a Hamiltonian. The ordinary differential equations (characteristic equations) defined by this function describe a dynamical system on the hypersurface. Its orbits can be used to reconstruct the equations of state. The ‘time’ variable associated to this dynamics is related to, but is not identical to, entropy. After developing this formalism on well-grounded systems such as the van der Waals gases and the Curie-Weiss magnets, we derive a Hamilton-Jacobi equation for black hole thermodynamics in General Relativity. The cosmological constant appears as a constant of integration in this picture.     

The pauli principle for a quantum theory on T with magnetic field

We discuss the reducible representation of n particles on a torus with magnetic field, where the gauge automorphisms are unitarily implementable. This representation is of type II_∞, if B is not integer. We show that there is a natural splitting into I_∞ ⊗ II₁ such that the Pauli exclusion principle acts only in the first factor. Under this condition we estimate the ground state energy for several particles and show that in the thermodynamic limit we obtain the correct result.     

Two magnetic impurities with arbitrary spins in open boundary t-J model

From the open boundary t-J model an impurity model is constructed in which magnetic impurities of arbitrary spins are coupled to the edges of the strongly correlated electron system. The boundary R matrices are given explicitly. The interaction parameters between magnetic impurities and electrons are related to the potentials of the impurities to preserve the integrability of the system. The Hamiltonian of the impurity model is diagonalized exactly. The integral equations of the ground state are derived and the ground state properties are discussed in detail. We discuss also the string solutions of the Bethe ansatz equations, which describe the bound states of the charges and spins. By minimizing the thermodynamic potential we get the thermodynamic Bethe ansatz equations. The finite size correction of the free energy contributed by the magnetic impurities is obtained explicitly. The properties of the system at some special limits are discussed and the boundary bound states are obtained.     

Configurations and observables in an Ising model with heat flow

We study a two dimensional Ising model between thermostats at different temperatures. By applying the recently introduced KQ dynamics, we show that the system reaches a steady state with coexisting phases transversal to the heat flow. The relevance of such complex states on thermodynamic or geometrical observables is investigated. In particular, we study energy, magnetization and metric properties of interfaces and clusters which, in principle, are sensitive to local features of configurations. With respect to equilibrium states, the presence of the heat flow amplifies the fluctuations of both thermodynamic and geometrical observables in a domain around the critical energy. The dependence of this phenomenon on various parameters (size, thermal gradient, interaction) is discussed also with reference to other possible diffusive models.     

2D quantum spin models and Jordan-Wigner fermions

We apply the 2D Jordan-Wigner fermionization to examine the ground state and thermodynamic properties of the square-lattice s=1/2 anisotropic XY model. We compare our findings with the results of different analytical and numerical approaches.     

Ground state energy for a model gas in one dimension

Ground state energies of many-body systems in one dimension in the thermodynamic limit are calculated. We use relations between the ground state energy and the scattering phase, which are exact for a delta-function potential, and are fulfilled approximately for other interactions. This will be applied to a model of quantum field theory, for which theS-matrix can be calculated exactly by means of a property which is called factorization.     

Core-halo distribution in the Hamiltonian mean-field model

We study a paradigmatic system with long-range interactions: the Hamiltonian mean-field (HMF) model. It is shown that in the thermodynamic limit this model does not relax to the usual equilibrium Maxwell-Boltzmann distribution. Instead, the final stationary state has a peculiar core-halo structure. In the thermodynamic limit, HMF is neither ergodic nor mixing. Nevertheless, we find that using dynamical properties of Hamiltonian systems it is possible to quantitatively predict both the spin distribution and the velocity distribution functions in the final stationary state, without any adjustable parameters. We also show that HMF undergoes a nonequilibrium first-order phase transition between paramagnetic and ferromagnetic states.     

A model for coexistent superconductivity and ferromagnetism

We explore the various temperature dependences and thermodynamic quantities of a mean-field model of a ferromagnetic–superconducting system. The starting point for this model is based on an s-wave pairing scheme in the singlet channel of the superconducting state and a spontaneously broken-symmetry phase in the ferromagnetic state. We show numerically and analytically that a state of coexistence reveals itself and is favoured energetically over other possible states, and a simple phase diagram is developed. Finally, a comparison of the specific heat with experiment is shown.     

High temperature superfluidity with abnormal fermionic occupancy

We examine a Lipkin based two-level pairing model at finite temperature and in the thermodynamic limit. Whereas at T=0 the model exhibits a superconducting ground state for sufficiently high values of the coupling constant, a partially superconducting phase in whichsome of the particles are paired, is found to survive at high temperatures in a special treatment. This phase is a mixture of “abnormally-occupied” eigenstates, which lie at higher energy, of the interactionless model Hamiltonian.     

Detection of possible density isomers by means of high energy reaction products

We present a drastic effect in the cross section of high energy target fragments caused by a possible density isomer in the nuclear equation of state. The fluid dynamical model used here contains dissipative processes such as shear viscosity and heat conduction as well as a thermodynamic evaporation model at a late stage of the nuclear collision. In our calculations we consider as an example the reaction Ne+U at an impact parameterb=4 fm.     

Maximum entropy with fluctuating constraints: The example of K-distributions

We indicate that in a maximum entropy setting, the thermodynamic β and the observation constraint are linked, so that fluctuations of the latter imposes fluctuations of the former. This gives an alternate viewpoint to ‘superstatistics’. While a Gamma model for fluctuations of the β parameter gives the so-called Tsallis distributions, we work out the case of a Gamma model for fluctuations of the observable, and show that this leads to K-distributions. We draw attention to the fact that these heavy-tailed distributions have high interest in physical applications, and we discuss them in some details.     

Resonance states in an effective chiral hadronic model

With an effective chiral flavour SU(3) model we show the effect of hadronic resonances on the QCD phase diagram. We state that varying the resonance couplings to the scalar and vector fields affects the order and location of the phase transition, the possible existence of a critical end point (CEP), and the thermodynamic properties. We present (strange) quark number susceptibilities at zero baryochemical potential and at three different points at the phase transition. Comparing results to lattice QCD, we state that reasonable large vector couplings limit the phase transition to a smooth crossover ruling out a CEP.