Related papers: Efficient sampling and counting algorithms for the…
We apply a newly proposed Monte Carlo method, the Wang-Landau algorithm, to the study of the three-dimensional antiferromagnetic q-state Potts models on a simple cubic lattice. We systematically study the phase transition of the models with…
The phase transition of a random mixed-bond Ising ferromagnet on a cubic lattice model is studied both numerically and analytically. In this work, we use the Cluster algorithms of Wolff and Glauber to simulate the dynamics of the system. We…
Phase transition in the two-dimensional $q$-state Potts model with random ferromagnetic couplings in the large-q limit is conjectured to be described by the isotropic version of the infinite randomness fixed point of the random…
We establish a general framework for developing approximation algorithms for a class of counting problems. Our framework is based on the cluster expansion of abstract polymer models formalism of Koteck\'y and Preiss. We apply our framework…
In this paper with study phase transitions of the $q$-state Potts model, through a number of unsupervised machine learning techniques, namely Principal Component Analysis (PCA), $k$-means clustering, Uniform Manifold Approximation and…
We present here two novel algorithms for simulated tempering simulations, which break detailed balance condition (DBC) but satisfy the skewed detailed balance to ensure invariance of the target distribution. The irreversible methods we…
A linear-time algorithm is presented for the construction of the Gibbs distribution of configurations in the Ising model, on a quantum computer. The algorithm is designed so that each run provides one configuration with a quantum…
Spin glasses are fundamental probability distributions at the core of statistical physics, the theory of average-case computational complexity, and modern high-dimensional statistical inference. In the mean-field setting, we design…
An exact analytical solution of generalized three-state double-chain Potts model with multi-spin interactions which are invariant under cyclic shift of all spin values is obtained. The partition function in a finite cyclically closed strip…
We study the performance of Markov chains for the $q$-state ferromagnetic Potts model on random regular graphs. It is conjectured that their performance is dictated by metastability phenomena, i.e., the presence of "phases" (clusters) in…
We describe an efficient Monte Carlo algorithm using a random walk in energy space to obtain a very accurate estimate of the density of states for classical statistical models. The density of states is modified at each step when the energy…
Grouping objects into clusters based on similarities or weights between them is one of the most important problems in science and engineering. In this work, by extending message passing algorithms and spectral algorithms proposed for…
We give a new sampling algorithm for the Potts model based on the Fortuin-Kasteleyn transformation. The method produces independent samples and sums up a large number of configurations for each sweep. The partition function and…
We discuss a method based on sampling minimally entangled typical thermal states (METTS) that can simulate finite temperature quantum systems with a computational cost comparable to ground state DMRG. Detailed implementations of each step…
The Markov entropy decomposition (MED) is a recently-proposed, cluster-based simulation method for finite temperature quantum systems with arbitrary geometry. In this paper, we detail numerical algorithms for performing the required steps…
We study the antiferromagnetic Potts model on the Poissonian Erd\"os-R\'enyi random graph. By identifying a suitable interpolation structure and an extended variational principle, together with a positive temperature second-moment analysis…
We consider the anti-ferromagnetic Potts model on the the integer lattice Z^2. The model has two parameters, q, the number of spins, and \lambda=\exp(-\beta), where \beta is ``inverse temperature''. It is known that the model has strong…
A cluster algorithm formulated in continuous (imaginary) time is presented for Ising models in a transverse field. It works directly with an infinite number of time-slices in the imaginary time direction, avoiding the necessity to take this…
Monte Carlo algorithms, like the Swendsen-Wang and invaded-cluster, sample the Ising and Potts models asymptotically faster than single-spin Glauber dynamics do. Here, we generalize both algorithms to sample Potts lattice gauge theory by…
We revisit the classic thermodynamic problem of maximum work extraction from two arbitrary sized hot and cold reservoirs, modelled as perfect gases. Assuming ignorance about the extent to which the process has advanced, which implies an…