Related papers: Interaction Order Estimation in Tensor Curie-Weiss…
We consider the Gibbs measure of a general interacting particle system for a certain class of ``weakly interacting" kernels. In particular, we show that the local point process converges to a Poisson point process as long as the inverse…
We consider a model for thermal contact through a diathermal interface between two macroscopic bodies at different temperatures: an Ising spin chain with nearest neighbor interactions is endowed with a Glauber dynamics with different…
We study the fluctuation problems at high temperature in the general mixed $p$-spin glass models under the weak external field assumption: $h= \rho N^{-\alpha}, \rho>0, \alpha \in [1/4,\infty]$. By extending the cluster expansion approach…
The Ising model with ferromagnetic interactions that decay as $1/r^\alpha$ is analyzed in the non-extensive regime $0\leq\alpha\leq d$, where the thermodynamic limit is not defined. In order to study the asymptotic properties of the model…
The Wigner spiked model in a mismatched setting is studied with the finite temperature Statistical Mechanics approach through its representation as a Sherrington-Kirkpatrick model with added Mattis interaction. The exact solution of the…
Limit theorems for the magnetization in the $p$-spin Curie-Weiss model, for $p \geq 3$, has been derived recently by Mukherjee et al. (2021). In this paper, we strengthen these results by proving Cram\'er-type moderate deviation theorems…
We study the random field $p$-spin model with Ising spins on a fully connected graph using the theory of large deviations in this paper. This is a good model to study the effect of quenched random field on systems which have a sharp first…
The emergence of global order in complex systems with locally interacting components is most striking at criticality, where small changes in control parameters result in a sudden global re-organization. We introduce a measure of…
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…
We consider the problem of learning the underlying graph of an unknown Ising model on p spins from a collection of i.i.d. samples generated from the model. We suggest a new estimator that is computationally efficient and requires a number…
We study the Hopfield model with pure $p$-spin interactions with even $p\geq 4$, and a number of patterns, M(N) growing with the system size, $N$, as $M(N) = \a N^{p-1}$. We prove the existence of a critical temperature $\b_p$ characterized…
The Quantum Heisenberg Ferromagnet can be naturally reformulated in terms of interacting bosons (called spin waves or magnons) as an expansion in the inverse spin size. We calculate the first order interaction correction to the free energy,…
A thermal-model analysis of particle production of p-p collisions at sqrt(s) = 17 GeV using the latest available data is presented. The sensitivity of model parameters on data selections and model assumptions is studied. The system-size…
We show that an high temperature expansion at fixed order parameter can be derived for the quantum Ising model. The basic point is to consider a statistical generating functional associated to the local spin state. The probability at…
The problem of inferring pair-wise and higher-order interactions in complex systems involving large numbers of interacting variables, from observational data, is fundamental to many fields. Known to the statistical physics community as the…
A combinatorial approach is used to study the critical behavior of a $q$-state Potts model with a round-the-face interaction. Using this approach it is shown that the model exhibits a first order transition for $q>3$. A second order…
Let $(W,W')$ be an exchangeable pair. Assume that \[E(W-W'|W)=g(W)+r(W),\] where $g(W)$ is a dominated term and $r(W)$ is negligible. Let $G(t)=\int_0^tg(s)\,ds$ and define $p(t)=c_1e^{-c_0G(t)}$, where $c_0$ is a properly chosen constant…
The $CP^1$ model with Hopf interaction is quantised following the Batalin-Tyutin (BT) prescription. In this scheme, extra BT fields are introduced which allow for the existence of only commuting first-class constraints. Explicit expression…
This paper studies a generalization of the Curie-Weiss model (the Ising model on a complete graph) to quantum mechanics. Using a natural probabilistic representation of this model, we give a complete picture of the phase diagram of the…
Systems of highly degenerate ordered or frozen state may exhibit inverse melting (reversible crystallization upon heating) or inverse freezing (reversible glass transition upon heating). This phenomena is reviewed, and a list of…