Related papers: Local Central Limit Theorem for Multi-Group Curie-…

We obtain rates of convergence in limit theorems of partial sums $S_n$ for certain sequences of dependent, identically distributed random variables, which arise naturally in statistical mechanics, in particular, in the context of the…

We study the fluctuations of the spin per site around the thermodynamic magnetization in the mean-field Blume-Capel model. Our main theorem generalizes the main result in a previous paper (Ellis, Machta, and Otto) in which the first…

In this paper we study the moderate deviations for the magnetization of critical Curie-Weiss model. Chen, Fang and Shao considered a similar problem for non-critical model by using Stein method. By direct and simple arguments based on…

How a system initially at infinite temperature responds when suddenly placed at finite temperatures is a way to check the existence of phase transitions. It has been shown in [R. da Silva, IJMPC 2023] that phase transitions are imprinted in…

We use a generalized form of Dyson's spin wave formalism to prove several central limit theorems for the large-spin asymptotics of quantum spins in a coherent state.

In this short note, we prove a central limit theorem for the free energy in the Ghatak- Sherrington model at high enough temperatures, based on a generalization of the stochastic calculus method for the SK model derived in [CN95, Tin05].

We consider a system with randomly layered ferromagnetic bonds (McCoy-Wu model) and study its critical properties in the frame of mean-field theory. In the low-temperature phase there is an average spontaneous magnetization in the system,…

Given a Coxeter system of large type we prove a non--commutative central limit theorem: After normalisation with the square root of n the characteristic function of the set of the first n generators tends in distribution to Wigners…

A novel mean-field approximation for quasi-one-dimensional (Q1D) quantum magnets is formulated. Our new mean-field approach is based on the Bethe-type effective-field theory, where thermal and quantum fluctuations between the…

Using an averaged generating function for coloured hard-dimers, some random variables of interest are studied. The main result lies in the fact that all their probability distributions obey a central limit theorem.

We extend the notion of Gibbsianness for mean-field systems to the set-up of general (possibly continuous) local state spaces. We investigate the Gibbs properties of systems arising from an initial mean-field Gibbs measure by application of…

Hambly, Keevash, O'Connell and Stark have proven a central limit theorem for the characteristic polynomial of a permutation matrix with respect to the uniform measure on the symmetric group. We generalize this result in several ways. We…

This paper proposes a conditional Curie-Weiss model as a model for opinion formation in a society polarized along two opinions, say opinions 1 and 2. The model comes with interaction strength $\beta>0$ and bais $h$. Here the population in…

The aim of this work is to put forward a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. After showing the formal equivalence linking econometric multinomial logit models to equilibrium…

At low temperatures, a spin ice enters a Coulomb phase - a state with algebraic correlations and topologically constrained spin configurations. In Ho2Ti2O7, we have observed experimentally that this process is accompanied by a non-standard…

The applicability conditions of a recently reported Central Limit Theorem-based approximation method in statistical physics are investigated and rigorously determined. The failure of this method at low and intermediate temperature is proved…

We consider the imitative monomer-dimer model on the complete graph introduced in [1]. It was understood that this model is described by the monomer density and has a phase transition along certain critical line. By reverting the model to a…

We investigate numerically and analytically the heating process in ergodic clusters of interacting spins 1/2 subjected to periodic pulses of external magnetic field. Our findings indicate that there is a threshold for the pulse strength…

Self consistent renormalization theory of itinerant ferromagnets is used to calculate the Curie temperature of clusters down to approximately 100 atoms in size. In these clusters the electrons responsible for the magnetic properties are…

We revisit the central limit theorem for integrated periodograms, equivalently for Toeplitz quadratic forms of stationary Gaussian sequences. Under a regular-variation assumption allowing long-memory singularities and slowly varying…