Related papers: Partition function for several Ising model interfa…
The recently introduced nested sampling algorithm allows the direct and efficient calculation of the partition function of atomistic systems. We demonstrate its applicability to condensed phase systems with periodic boundary conditions by…
The intrinsic excitation energy of fission fragments is dynamically evaluated in terms of the time dependent pairing equations. These equations are corroborated with two conditions. One of them fixes the number of particles and the another…
A scaling description is obtained for the $d$--dimensional random field Ising model from domains in a bar geometry. Wall roughening removes the marginality of the $d=2$ case, giving the $T=0$ correlation length $\xi \sim \exp\left(A…
We present an exact solution to an interface model representing the dynamics of a domain wall in a two-phase Ising system. The model is microscopically motivated, yet we find that in the scaling regime our results are consistent with those…
Finite size effects for the Ising Model coupled to two dimensional random surfaces are studied by exploiting the exact results from the 2-matrix models. The fixed area partition function is numerically calculated with arbitrary precision by…
Calculating relative free energies is a topic of substantial interest and has many applications including solvation and binding free energies, which are used in computational drug discovery. However, there remain the challenges of accuracy,…
We consider the problem of approximating partition functions for Ising models. We make use of recent tools in combinatorial optimization: the Sherali-Adams and Lasserre convex programming hierarchies, in combination with variational methods…
Recently B. Derrida [Phys. Rev. E 55, 3705 (1997)] introduced a numerical technique that allows one to measure the fraction of persistent spins in a coarsening nonequilibrium system at finite temperature. In the present work we extend this…
Finite size corrections to the pressure (free energy) of the Ising model on a 2 dimensional cylinder are calculated and shown to be consistent with the predictions of conformal field theory. The exact solution of the model is expressed in…
We discuss finite difference techniques for hyperbolic equations in non-trivial domains, as those that arise when simulating black hole spacetimes. In particular, we construct dissipative and difference operators that satisfy the {\it…
This paper proposes a gradient descent based optimization method that relies on automatic differentiation for the computation of gradients. The method uses tools and techniques originally developed in the field of artificial neural networks…
The scaling limit of the two-dimensional Ising model in the plane of temperature and magnetic field defines a field theory which provides the simplest illustration of non-trivial phenomena such as spontaneous symmetry breaking and…
The zero-field partition function of two-dimensional nearest neighbor Ising models of square lattices is derived in terms of the generalized hypergeometric series by evaluating the integral in the exact solution of Onsager. An approximate…
Generating functions for plane overpartitions are obtained using various methods such as nonintersecting paths, RSK type algorithms and symmetric functions. We extend some of the generating functions to cylindric partitions. Also, we show…
A new and efficient algorithm is presented for the calculation of the partition function in the $S=\pm 1$ Ising model. As an example, we use the algorithm to obtain the thermal dependence of the magnetic spin susceptibility of an Ising…
This paper shows that the plane wave expansion can be a useful tool in obtaining analytical solutions to infinite integrals over spherical Bessel functions and the derivation of identites for these functions. The integrals are often used in…
The microscopic approach to calculating the free energy of a three-dimensional Ising-like system in a homogeneous external field is developed in the higher non-Gaussian approximation (the $\rho^6$ model) at temperatures above the critical…
Computing the partition function and the marginals of a global probability distribution are two important issues in any probabilistic inference problem. In a previous work, we presented sub-tree based upper and lower bounds on the partition…
We present a general, rigorous theory of partition function zeros for lattice spin models depending on one complex parameter. First, we formulate a set of natural assumptions which are verified for a large class of spin models in a…
In many systems, the time scales of the microscopic dynamics and macroscopic dynamics of interest are separated by many orders of magnitude. Examples abound, for instance nucleation, protein folding, and chemical reactions. For these…