Related papers: The Free Energy Formula
The applicability of the Lifshitz formula is discussed to the case of two thick parallel plates made of real metal. The usual description of the zero-point vacuum oscillations on the background of the frequency-dependent dielectric…
One-dimensional free boundary problem for a nonlinear diffusion - convection equation with a Dirichlet condition at fixed face $x=0$, variable in time, is considered. Throught several transformations the problem is reduced to a free…
We present a lattice Boltzmann algorithm based on an underlying free energy that allows the simulation of the dynamics of a multicomponent system with an arbitrary number of components. The thermodynamic properties, such as the chemical…
In this paper we study multi-matrix models whose potentials are perturbations of the quadratic potential associated with independent GUE random matrices. More precisely, we compute the free energy and the expectation of the trace of…
After briefly reviewing how the (proper-time) Schwinger's formula works for computing the Casimir energy in the case of "scalar electrodynamics" where the boundary conditions are dictated by two perfectly conducting parallel plates with…
The Peierls argument is a mathematically rigorous and intuitive method to show the presence of a non-vanishing spontaneous magnetization in some lattice models. This argument is typically explained for the $D=2$ Ising model in a way which…
We consider the quantum ferromagnetic Heisenberg model in three dimensions, for all spins $S\geq 1/2$. We rigorously prove the validity of the spin-wave approximation for the excitation spectrum, at the level of the first non-trivial…
We consider a free $p$-form gauge theory on a $d$-dimensional sphere of radius $R$ and calculate its free energy. We perform the calculation for generic values of $p$ and obtain the free energy as a function of $d, p$ and $R$. The result…
We have analyzed data on the free ion yield observed in liquid isooctane irradiated by Co60 gamma rays within the framework of the Onsager theory about initial recombination. Several distribution functions describing the electron…
We calculate the energy and wave functions of two particles confined to two spatial dimensions interacting via arbitrary anisotropic potentials with negative or zero net volume. The general rigorous analytic expressions are given in the…
Properties of an infinite system of nonlinearly coupled ordinary differential equations are discussed. This system models some properties present in the equations of motion for an inviscid fluid such as the skew symmetry and the…
This paper tests a dielectric model for variation of hydration free energy with geometry of complex solutes in water. It works out some basic aspects of the theory of boundary integral methods for these problems. One aspect of the…
We consider (2+1)-QFT at finite temperature on a product of time with a static spatial geometry. The suitably defined difference of thermal vacuum free energy for the QFT on a deformation of flat space from its value on flat space is a UV…
We study the critical Ising model with free boundary conditions on finite domains in $\mathbb{Z}^d$ with $d\geq4$. Under the assumption, so far only proved completely for high $d$, that the critical infinite volume two-point function is of…
We study the two-dimensional massless Dirac equation for a potential that is allowed to depend on the energy and on one of the spatial variables. After determining a modified orthogonality relation and norm for such systems, we present an…
We prove the Freiheitssatz for the variety of generic Poisson algebras.
Given a consistent choice of conformally invariant boundary conditions in a two dimensional conformal field theory, one can construct new consistent boundary conditions by deforming with a relevant boundary operator and flowing to the…
We consider the interacting Bose gas in the thermodynamic limit in a large box in $\R^d$ at positive temperature $1/\beta\in(0,\infty)$ with particle density $\sim\rho\in(0,\infty)$. We follow a path-integral approach and adopt from \cite…
We consider a Bose gas at density $\rho > 0$, interacting through a repulsive potential $V \in L^2 (\mathbb{R}^3)$ with scattering length $\mathfrak{a} > 0$. We prove an upper bound for the free energy of the system, valid at low…
This work proves an upper bound for the free energy of the Sherrington-Kirkpatrick model and its generalizations in terms of the Thouless-Anderson-Palmer (TAP) energy. The result applies to models with spherical or Ising spins and any mixed…