Related papers: FPTAS for Hardcore and Ising Models on Hypergraphs
We consider the problem of approximating the partition function of the hard-core model on planar graphs of degree at most 4. We show that when the activity lambda is sufficiently large, there is no fully polynomial randomised approximation…
The task of exploring and understanding various aspects of far-from-equilibrium dynamics of closed and generic quantum many-body systems has received a thrust of attention in recent years, driven partly by remarkable advances in ultracold…
In this study the magnetization phenomenon has been investigated as a behavior of interacting elementary moments ensemble, with the help of Ising model [1] in the frame of non-extensive statistical mechanics. To investigate the physical…
Based on the path integral representation of the partition function of a many body system with separable two body interaction we propose a systematic extension of the perturbed static path approximation (PSPA) to lower temperatures.…
A spin system is a framework in which the vertices of a graph are assigned spins from a finite set. The interactions between neighbouring spins give rise to weights, so a spin assignment can also be viewed as a weighted graph homomorphism.…
The s=1/2 Ising chain with uniform nearest-neighbor and next-nearest-neighbor coupling is used to construct a system of floating particles characterized by motifs of up to six consecutive local spins. The spin couplings cause the assembly…
In VLSI physical design, many algorithms require the solution of difficult combinatorial optimization problems such as max/min-cut, max-flow problems etc. Due to the vast number of elements typically found in this problem domain, these…
There is no an accepted exact partition function (PF) for the two-dimensional (2D) Ising model with a non-zero external magnetic field to our knowledge. Here we infer an empirical PF for such an Ising model. We compare the PFs for two…
Ising models, and the physical systems described by them, play a central role in generating entangled states for use in quantum metrology and quantum information. In particular, ultracold atomic gases, trapped ion systems, and Rydberg atoms…
We study a family of inhomogeneous Ising chain models along with an equivalent family of nearest neighbour particle systems. By the correspondence between the two families we prove identities of combinatorial significance relating to…
Recent developments have highlighted the potential of quantum spin models to realize the phenomenology of confinement leading to the formation of bound states such as mesons. In this work we show that Ising chains also provide a platform to…
The key problem of statistical physics standing over one hundred years is how to exactly calculate the partition function (or free energy) of many-body interaction systems, which severely hinders application of the theory for realistic…
The data-driven characterization of the ``complexity'' present in dynamical systems remains an open problem with broad applications across the physical sciences. We investigate the ``structural complexity'' of the 2D ferromagnetic Ising…
We design a fully polynomial time approximation scheme (FPTAS) for counting the number of matchings (packings) in arbitrary 3-uniform hypergraphs of maximum degree three, referred to as $(3,3)$-hypergraphs. It is the first polynomial time…
We study the two-dimensional square lattice Ising ferromagnet and antiferromagnet with a magnetic field by using tensor network method. Focusing on the role of guage fixing, we present the partition function in terms of a tensor network.…
The approach is developed for the description of isolated Fermi-systems with finite number of particles, such as complex atoms, nuclei, atomic clusters etc. It is based on statistical properties of chaotic excited states which are formed by…
The partition function of a factor graph and the partition function of the dual factor graph are related to each other by the normal factor graph duality theorem. We apply this result to the classical problem of computing the partition…
We develop a model based on the fractional exclusion statistics (FES) applicable to non-homogeneous interacting particle systems. Here the species represent elementary volumes in an (s+1)-dimensional space, formed by the direct product…
We study the problem of deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model…
In this survey, we give a friendly introduction from a graph theory perspective to the q-state Potts model, an important statistical mechanics tool for analyzing complex systems in which nearest neighbor interactions determine the aggregate…