Related papers: Graphical representations and cluster algorithms f…
We study the continuum scaling limit of the critical Ising magnetization in two dimensions. We prove the existence of subsequential limits, discuss connections with the scaling limit of critical FK clusters, and describe work in progress of…
This paper presents a model for a dynamical system where particles dominate edges in a complex network. The proposed dynamical system is then extended to an application on the problem of community detection and data clustering. In the case…
Recently, spatial photonic Ising machines (SPIM) have been demonstrated to compute the minima of Hamiltonians for large-scale spin systems. Here we propose to implement an antiferromagnetic model through optoelectronic correlation computing…
Based on conformal symmetry we propose an exact formula for the four-point connectivities of FK clusters in the critical Ising model when the four points are anchored to the boundary. The explicit solution we found displays logarithmic…
In a statistical cluster or loop model such as percolation, or more generally the Potts models or O(n) models, a pinch point is a single bulk point where several distinct clusters or loops touch. In a polygon P harboring such a model in its…
An InfoCGAN neural network is trained on 2-dimensional square Ising configurations conditioned on the external applied magnetic field and the temperature. The network is composed of two main sub-networks. The generator network learns to…
We consider the problem of estimating the partition function of the ferromagnetic Ising model in a consistent external magnetic field. The estimation is done via importance sampling in the dual of the Forney factor graph representing the…
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…
Topological analysis of the magnetic field in simulated plasmas allows the study of various physical phenomena in a wide range of settings. One such application is magnetic reconnection, a phenomenon related to the dynamics of the magnetic…
Improving the explainability of the results from machine learning methods has become an important research goal. Here, we study the problem of making clusters more interpretable by extending a recent approach of [Davidson et al., NeurIPS…
In this paper we lay special stress on analyzing the topological properties of the lattice systems and try to ovoid the conventional ways to calculate the critical points. Only those clusters with finite sizes can execute the self similar…
In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature/energy range around the critical point. By combining the replica-exchange algorithm with cluster updates…
Based on the connection between the Ising model and a correlated percolation model, we calculate the distribution function for the fraction ($c$) of lattice sites in percolating clusters in subgraphs with $n$ percolating clusters, $f_n(c)$,…
We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs. We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions…
We present an algorithm for cluster dynamics to efficiently simulate large systems on MIMD parallel computers with large numbers of processors. The method divides physical space into rectangular cells which are assigned to processors and…
The scaling of correlations as a function of system size provides important hints to understand critical phenomena on a variety of systems. Its study in biological systems offers two challenges: usually they are not of infinite size, and in…
We present an optimized version of a cluster labeling algorithm previously introduced by the authors. This algorithm is well suited for large-scale Monte Carlo simulations of spin models using cluster dynamics on parallel computers with…
We study a cluster Ising model with non-Hermitian external field which can be exactly solved in the language of free fermions. By investigating the second derivative of energy density and fidelity, the possible new critical points are…
The finite size scaling behaviour for the Ising model in five dimensions, with either free or cyclic boundary, has been the subject for a long running debate. The older papers have been based on ideas from e.g. field theory or…
We first present an empirical study of the Belief Propagation (BP) algorithm, when run on the random field Ising model defined on random regular graphs in the zero temperature limit. We introduce the notion of maximal solutions for the BP…