Related papers: Modified rational six vertex model on a rectangula…
An $n$-dimensional generalization of the Onsager Ising partition function integral is reduced to a single integral and applied to evaluate the partition function and residual entropy of an eight vertex model.
A class of fast-slow Hamiltonian systems with potential $U_\varepsilon$ describing the interaction of non-ergodic fast and slow degrees of freedom is studied. The parameter $\varepsilon$ indicates the typical timescale ratio of the fast and…
Using the exact propagators in a constant magnetic field, the effective electromagnetic Lagrangian at finite temperature and density is calculated to all orders in the field strength B within the framework of the complete electroweak model,…
Partial energy fluctuations are known tools to reconstruct microcanonical heat capacities. For experimental applications, approximations have been developed to infer fluctuations at freeze out from the observed fragment partitions. The…
Lattice kinetic equations incorporating the effects of external/internal force fields via a shift of the local fields in the local equilibria, are placed within the framework of continuum kinetic theory. The mathematical treatment reveals…
We propose a new formulation of stochastic thermodynamics for systems subjected to nonequilibrium constraints (i.e. broken detailed balance at steady state) and furthermore driven by external time-dependent forces. A splitting of the second…
Different formulas relying measurable fragment isotopic observables to the symmetry energy of excited nuclei have been proposed and applied to the analysis of heavy ion collision data in the recent literature. In this paper we examine the…
The melting transition of the vortex lattice in highly anisotropic, layered superconductors with commensurate, periodic columnar pins is studied in a geometry where magnetic field and columnar pins are normal to the layers. Thermodynamic…
For the calculation of the partition function $\mathcal{Z}$ of small, isolated and interacting many body systems an improvement with respect to previous formulations is presented. By including anharmonicities and employing a variational…
We consider the six-vertex model with the rational weights on an $s\times N$ square lattice, $s\leq N$, with partial domain wall boundary conditions. We study the one-point function at the boundary where the free boundary conditions are…
We present a Hilbert space perspective to homogenization of standard linear evolutionary boundary value problems in mathematical physics and provide a unified treatment for (non-)periodic homogenization problems in thermodynamics,…
In 1944 Onsager published the formula for the partition function of the Ising model for the infinite square lattice. He was able to express the internal energy in terms of a special function, but he left the free energy as a definite…
We investigate the convergence properties of finite-temperature perturbation theory by considering the mathematical structure of thermodynamic potentials using complex analysis. We discover that zeros of the partition function lead to poles…
Partition function zeros are powerful tools in understanding critical behavior. In this paper we present new results of the Fisher zeros of two-dimensional Ising models, in the framework of free-fermion eight-vertex model. First we succeed…
For the system with inhomogeneous distribution of macroscopic parameters we obtain thermodynamic relation which depends on the spatial point (coordinate). In our approach, to obtain such a relation we use the basic ideas of the method of…
In this paper we investigate some particular spin lattice (a higher dimensional generalization of a spin chain) related to Zamolodchikov model, in the limit when both sizes of the lattice tend to infinity. An infinite set of bilinear…
Volume and enthalpy relaxation of glasses after a sudden temperature change has been extensively studied since Kovacs seminal work. One observes an asymmetric approach to equilibrium upon cooling versus heating and, more…
We first study a free particle on an $(n-1)$-sphere in an extended phase space, where the originally second-class Hamiltonian and constraints are now in strong involution. This allows for a Schr\"odinger representation and a Hamilton-Jacobi…
We study limit shapes in two equivalent models: the six-vertex model in the $c\to0$ limit and the random Mallows permutation with restricted permutation matrix. We give the Euler-Lagrange equation for the limit shape and show how to solve…
We study numerically the density profile in the six-vertex model with domain wall boundary conditions. Using a Monte Carlo algorithm originally proposed by Allison and Reshetikhin we numerically evaluate the inhomogeneous density profiles…