Related papers: The Ising model on cubic maps: arbitrary genus
We propose a method for generalizing the Ising model in magnetic fields and calculating the partition function (exact solution) for the Ising model of an arbitrary shape. Specifically, the partition function is calculated using matrices…
We consider a refinement of the partition function of graph homomorphisms and present a quasi-polynomial algorithm to compute it in a certain domain. As a corollary, we obtain quasi-polynomial algorithms for computing partition functions…
We characterize the generating function of bipartite planar maps counted according to the degree distribution of their black and white vertices. This result is applied to the solution of the hard particle and Ising models on random planar…
We establish the average-case hardness of the algorithmic problem of exact computation of the partition function associated with the Sherrington-Kirkpatrick model of spin glasses with Gaussian couplings and random external field. In…
The aim of this short note is to draw attention to a method by which the partition function and marginal probabilities for a certain class of random fields on complete graphs can be computed in polynomial time. This class includes Ising…
We consider a family of quantum spin systems which includes as special cases the ferromagnetic XY model and ferromagnetic Ising model on any graph, with or without a transverse magnetic field. We prove that the partition function of any…
The fundamental aim of clustering algorithms is to partition data points. We consider tasks where the discovered partition is allowed to vary with some covariate such as space or time. One approach would be to use fragmentation-coagulation…
We study the complexity of approximately evaluating the Ising and Tutte partition functions with complex parameters. Our results are partly motivated by the study of the quantum complexity classes BQP and IQP. Recent results show how to…
We consider the task of learning Ising models when the signs of different random variables are flipped independently with possibly unequal, unknown probabilities. In this paper, we focus on the problem of robust estimation of…
We represent a general procedure for calculating the partition function of an Ising model on a one dimensional Fibonacci lattice in presence of magnetic field.This partition function can be written as a sum of partition functions of usual…
Given a family of rational curves depending on a real parameter, defined by its parametric equations, we provide an algorithm to compute a finite partition of the parameter space (${\Bbb R}$, in general) so that the shape of the family…
We study the problem of approximating the partition function of the ferromagnetic Ising model in graphs and hypergraphs. Our first result is a deterministic approximation scheme (an FPTAS) for the partition function in bounded degree graphs…
We show that the number of $k$-matching in a given undirected graph $G$ is equal to the number of perfect matching of the corresponding graph $G_k$ on an even number of vertices divided by a suitable factor. If $G$ is bipartite then one can…
Random matrix products arise in many science and engineering problems. An efficient evaluation of its growth rate is of great interest to researchers in diverse fields. In the current paper, we reformulate this problem with a generating…
We study mappings between distinct classical spin systems that leave the partition function invariant. As recently shown in [Phys. Rev. Lett. 100, 110501 (2008)], the partition function of the 2D square lattice Ising model in the presence…
We present a new family of zero-field Ising models over $N$ binary variables/spins obtained by consecutive "gluing" of planar and $O(1)$-sized components and subsets of at most three vertices into a tree. The polynomial-time algorithm of…
We find that the overlapping of a topological quantum color code state, representing a quantum memory, with a factorized state of qubits can be written as the partition function of a 3-body classical Ising model on triangular or Union Jack…
The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum system and phenomenon. However, for interacting many-body quantum systems, its…
Ising computing provides a new computing paradigm for many hard combinatorial optimization problems. Ising computing essentially tries to solve the quadratic unconstrained binary optimization problem, which is also described by the Ising…
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…