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Related papers: The Free Energy Formula

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For one-dimensional spin and pseudospin models that allow mapping to a Markov chain, the free energy of the system at a finite temperature can be expressed in terms of bond concentrations. Minimizing the free energy function makes it…

Statistical Mechanics · Physics 2025-12-01 Yu. D. Panov

We consider a possible `deformation' of the trace of the heat kernel on odd dimensional spheres, motivated by the calculation of the free energy of a scalar field on a discretized circle. By using an expansion in terms of the modified…

Mathematical Physics · Physics 2018-04-02 Nahomi Kan , Kiyoshi Shiraishi

We consider a binary system of small and large spheres of finite size in a continuous medium interacting via a non-negative potential. We work in the canonical ensemble and compute upper and lower bound for the free energy at finite and…

Mathematical Physics · Physics 2023-10-24 Tong Xuan Nguyen , Giuseppe Scola , Dimitrios Tsagkarogiannis

We obtain exact closed-form expressions for the partition function of the one-dimensional Ising model in the fixed-$M$ ensemble, for three commonly-used boundary conditions: periodic, antiperiodic and Dirichlet. These expressions allow for…

Statistical Mechanics · Physics 2022-11-30 Daniel Dantchev , Joseph Rudnick

Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal…

Statistical Mechanics · Physics 2015-05-27 Kurt Binder , Benjamin Block , Subir K. Das , Peter Virnau , David Winter

Within this work we derive and analyse an expression for the free energy of a single-species system in the thermodynamic limit in terms of a generalised cavity volume, that is exact in general, and in principle applicable to systems across…

Statistical Mechanics · Physics 2021-11-05 Jamie M. Taylor , Thomas G. Fai , Epifanio G. Virga , Xiaoyu Zheng , Peter Palffy-Muhoray

The purpose of this Comment is to show that the solutions to the zero energy Schr\"odinger equations for monomial central potentials discussed in a recently published Letter, may also be obtained from the corresponding free particle…

General Relativity and Quantum Cosmology · Physics 2016-08-15 Sergio A. Hojman , Darío Núñez

Massless scalar electrodynamics is studied at high temperature and zero chemical potential. I derive the free energy to order $\lambda^2$, $\lambda e^2$ and $e^4$ by effective field theory methods. The first step consists of the…

High Energy Physics - Phenomenology · Physics 2007-05-23 J. O. Andersen

We analyze the thermodynamics of the focusing discrete nonlinear Schr\"odinger equation in dimensions $d\ge 3$ with general nonlinearity $p>1$ and under a model with two parameters, representing inverse temperature and strength of the…

Analysis of PDEs · Mathematics 2023-01-19 Partha S. Dey , Kay Kirkpatrick , Kesav Krishnan

We present a unique derivation of metadynamics. The starting point for the derivation is an on-the-fly reweighting scheme but through an approximation we recover the standard metadynamics and the well-tempered metadynamics in a general form…

Statistical Mechanics · Physics 2011-11-10 Bradley M. Dickson

Starting for the Stillinger and Weber expression for the free energy of supercooled liquids, we extend the free energy to the case in which two time scales separate and the system is in quasi-equilibrium. The concept of an effective…

Soft Condensed Matter · Physics 2012-11-26 Antonio Scala , Francesco Sciortino

The explicit expression for the two-time free energy distribution function in one-dimensional directed polymers in random potential is derived in terms of the Bethe ansatz replica technique by mapping the replicated problem to the…

Statistical Mechanics · Physics 2013-08-12 Victor Dotsenko

We investigate relaxation dynamics along the entire first-order phase transition line by analyzing the time evolution of the free energy landscape in the three-dimensional kinetic Ising model. Near the critical temperature $T_{\rm c}$, the…

Statistical Mechanics · Physics 2025-08-28 Ranran Guo , Xiaobing Li , Yuming Zhong , Mingmei Xu , Jinghua Fu , Yuanfang Wu

We have found a simple criterion which allows for the straightforward determination of the order-disorder critical temperatures. The method reproduces exactly results known for the two dimensional Ising, Potts and $Z(N<5)$ models. It also…

High Energy Physics - Lattice · Physics 2009-10-22 J. Wosiek

The paper presents new method for calculating the low-temperature asymptotics of free energy of the 3D Ising model in external magnetic field $(H\neq 0)$. The results obtained are valid in the wide range of temperature and magnetic field…

Statistical Mechanics · Physics 2007-05-23 Martin S. Kochman'ski

We derive a new upper bound for the correlations in a heterogeneous one-dimensional Ising model with free boundary conditions. The new upper bound quantifies the simultaneous decay of correlations due to weakness of nearest-neighbor…

Probability · Mathematics 2026-02-10 Edward Athaide , Maciej Głuchowski , Jonas Köppl , Georg Menz

In this work we obtain the planar free energy for the Hermitian one-matrix model with various choices of the potential. We accomplish this by applying an approach that bypasses the usual diagonalization of the matrices and the introduction…

High Energy Physics - Theory · Physics 2022-03-02 Bartomeu Fiol , Alan Rios Fukelman

We study the boundary free energy of the XXZ spin-$\tf{1}{2}$ chain subject to diagonal boundary fields. We first show that the representation for its finite Trotter number approximant obtained by Bortz, Frahm and G\"{o}hmann is related to…

Exactly Solvable and Integrable Systems · Physics 2015-06-03 K. K. Kozlowski , B. Pozsgay

Estimating the free energy in molecular simulation requires, implicitly or explicitly, counting how many times the system is observed in a finite region. If the simulation is biased by an external potential, the weight of the configurations…

Chemical Physics · Physics 2021-12-22 Matteo Carli , Alessandro Laio

We compute the Casimir energy for a free scalar field on the spaces $\,R^{m+1}\,\times\,\tilde S^2\,$ where $,\tilde S^2\,$ is two-dimensional deformed two-sphere.

High Energy Physics - Theory · Physics 2016-09-06 N. ~Shtykov , D. ~V. ~Vassilevich