Related papers: Complex Random Energy Model: Zeros and Fluctuation…
We study a Brownian particle on a moving periodic potential. We focus on the statistical properties of the work done by the potential and the heat dissipated by the particle. When the period and the depth of the potential are both large, by…
The zeros of the partition function of the ferromagnetic q-state Potts model with long-range interactions in the complex-q plane are studied in the mean-field case, while preliminary numerical results are reported for the finite 1d chains…
In this paper, we consider a strongly-repelling model of $n$ ordered particles $\{e^{i \theta_j}\}_{j=0}^{n-1}$ with the density $p({\theta_0},\cdots, \theta_{n-1})=\frac{1}{Z_n} \exp \left\{-\frac{\beta}{2}\sum_{j \neq k} \sin^{-2} \left(…
Number partitioning is a classical problem from combinatorial optimisation. In physical terms it corresponds to a long range anti-ferromagnetic Ising spin glass. It has been rigorously proven that the low lying energies of number…
The partition function and specific heat of a system consisting of a finite number of bosons confined in an external potential are calculated in canonical ensemble. Using the grand partition function as the generating function of the…
We prove that the pressure (or free energy) of the finite range ferromagnetic Ising model on $\mathbb{Z}^d$ is analytic as a function of both the inverse temperature $\beta$ and the magnetic field $h$ whenever the model has the exponential…
We present exact calculations of the partition function $Z$ of the $q$-state Potts model and its generalization to real $q$, the random cluster model, for arbitrary temperature on $n$-vertex ladder graphs with free, cyclic, and M\"obius…
We consider the system of $N$ one-dimensional free fermions confined by a harmonic well $V(x) = m\omega^2 {x^2}/{2}$ at finite inverse temperature $\beta = 1/T$. The average density of fermions $\rho_N(x,T)$ at position $x$ is derived. For…
Among the statistical mechanical frameworks able to describe systems in non-equilibrium steady states such as collisionless plasmas, self-gravitating systems and other complex systems, superstatistics have gained recent attention.…
Thermodynamic properties can be in principle derived from the partition function, which, in many-atom systems, is hard to evaluate as it involves a sum on the accessible microscopic states. Recently, the partition function has been computed…
In this work we establish under certain hypotheses the $N \to +\infty$ asymptotic expansion of integrals of the form $$\mathcal{Z}_{N,\Gamma}[V] \, = \, \int_{\Gamma^N} \prod_{ a < b}^{N}(z_a - z_b)^\beta \, \prod_{k=1}^{N} \mathrm{e}^{ - N…
We study the partition function and free energy of the Curie-Weiss model with complex temperature, and partially describe its phase transitions. As a consequence, we obtain information on the locations of zeros of the partition function.
We extend the circle theorem on the zeros of the partition function to a continuum system. We also calculate the exact zeros of the partition function for a finite system where the probability distribution for the order parameter is given…
An approximate partition functional is derived for the infinite-dimensional Hubbard model. This functional naturally includes the exact solution of the Falicov-Kimball model as a special case, and is exact in the uncorrelated and atomic…
We present calculations of the complex-temperature zeros of the partition functions for 2D Ising models on the square lattice with spin $s=1$, 3/2, and 2. These give insight into complex-temperature phase diagrams of these models in the…
For a power series which converges in some neighborhood of the origin in the complex plane, it turns out that the zeros of its partial sums---its sections---often behave in a controlled manner, producing intricate patterns as they converge…
This note derives the various forms of entropy of systems subject to Olbert distributions (generalized Lorentzian probability distributions known as $\kappa$-distributions) which are frequently observed particularly in high temperature…
The number partitioning problem is a classic problem of combinatorial optimization in which a set of $n$ numbers is partitioned into two subsets such that the sum of the numbers in one subset is as close as possible to the sum of the…
We present an efficient sampling method for computing a partition function and accelerating configuration sampling. The method performs a random walk in the $\lambda$ space, with $\lambda$ being any thermodynamic variable that characterizes…
We study the partition function from random matrix theory using a well known connection to orthogonal polynomials, and a recently developed Riemann-Hilbert approach to the computation of detailed asymptotics for these orthogonal…