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The effects of competing quadrupolar- and spin-glass orderings are investigated on a spin-1 Ising model with infinite-range random $p$-spin interactions. The model is studied through the replica approach and a phase diagram is obtained in…
One of the outstanding challenges of cross-identification is multiplicity: detections in crowded regions of the sky are often linked to more than one candidate associations of similar likelihoods. We map the resulting maximum likelihood…
The multifractal properties of the Edwards-Anderson order parameter of the short-range Ising spin glass model on d=3 diamond hierarchical lattices is studied via an exact recursion procedure. The profiles of the local order parameter are…
While phases and phase transitions are conventionally described by local order parameters in real space, we present a unified framework characterizing the phase transition through the geometry of configuration space defined by the…
Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm for phase transitions in finite dimensions, describing ferromagnets and even some fluids…
We use the Binary Intrinsic Dimension (BID), a geometrical measure designed for binary data, to analyze the Hopfield model, a paradigmatic spin system from statistical mechanics, machine learning and neuroscience. The BID allows us to…
In a geometric inhomogeneous random graph vertices are given by the points of a Poisson process and are equipped with independent weights following a heavy tailed distribution. Any pair of distinct vertices is independently forming an edge…
We investigate the geometry of a typical spin cluster in random triangulations sampled with a probability proportional to the energy of an Ising configuration on their vertices, both in the finite and infinite volume settings. This model is…
We reconsider Ising spins in a Gaussian random field within the replica formalism. The corresponding continuum model involves several coupling constants beyond the single one which was considered in the standard $\phi^4$ theory approach.…
The nature of the ordering of the three-dimensional isotropic Heisenberg spin glass with nearest-neighbor random Gaussian coupling is studied by extensive Monte Carlo simulations. Several independent physical quantities are measured both…
We propose a method to evaluate parameters in the Hamiltonian of the Ising chain under site-dependent transverse fields, with a proviso that we can control and measure one of the edge spins only. We evaluate the eigenvalues of the…
Computing the ground state of Ising spin-glass models with p-spin interactions is, in general, an NP-hard problem. In this work we show that unlike in the case of the standard Ising spin glass with two-spin interactions, computing ground…
We investigate the depinning transition for driven interfaces in the random-field Ising model for various dimensions. We consider the order parameter as a function of the control parameter (driving field) and examine the effect of thermal…
A permutation statistic $\operatorname{st}$ is said to be shuffle-compatible if the distribution of $\operatorname{st}$ over the set of shuffles of two disjoint permutations $\pi$ and $\sigma$ depends only on $\operatorname{st}\pi$,…
For random percolation at p_c, the probability distribution P(n) of the number of spanning clusters (n) has been studied in large scale simulations. The results are compatible with $P(n) \sim \exp(-an^2)$ for all dimensions. We also study…
Two-dimensional bootstrap percolation is a cellular automaton in which sites become 'infected' by contact with two or more already infected nearest neighbors. We consider these dynamics, which can be interpreted as a monotone version of the…
Jigsaw percolation is a nonlocal process that iteratively merges connected clusters in a deterministic "puzzle graph" by using connectivity properties of a random "people graph" on the same set of vertices. We presume the Erdos--Renyi…
Max-stable processes are increasingly widely used for modelling complex extreme events, but existing fitting methods are computationally demanding, limiting applications to a few dozen variables. $r$-Pareto processes are mathematically…
A recent paper due to Duminil-Copin and Tassion from $2019$ introduces a novel argument for obtaining estimates on horizontal crossing probabilities of the Random-Cluster model, in which a range of four possible behaviors, through a…
The random field Ising model with Gaussian disorder is studied using a new Monte Carlo algorithm. The algorithm combines the advantanges of the replica exchange method and the two-replica cluster method and is much more efficient than the…