Related papers: Topics on abelian spin models and related problems
We introduce a general class of statistical-mechanics models, taking values in an abelian group, which includes examples of both spin and gauge models, both ordered and disordered. The model is described by a set of ``variables'' and a set…
To highlight certain similarities in combinatorial representations of several well known two-dimensional models of statistical mechanics, we introduce and study a new family of models which specializes to these cases after a proper tuning…
A brief review is given on the study of the thermodynamic properties of spin models defined on different topologies like small-world, scale-free networks, random graphs and regular and random lattices. Ising, Potts and Blume-Capel models…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
In this article we study the sharpness of the phase transition for percolation models defined on top of planar spin systems. The two examples that we treat in detail concern the Glauber dynamics for the Ising model and a Dynamic Bootstrap…
A problem of practical significance is the analysis of large, spatially distributed data sets. The problem is more challenging for variables that follow non-Gaussian distributions. We show that the spatial correlations between variables can…
We generalize the switching lemma of Griffiths, Hurst and Sherman to the random current representation of the Ashkin-Teller model. We then use it together with properties of two-dimensional topology to derive linear relations for…
We consider discrete spin models on arbitrary planar graphs and lattices with frustrated interactions. We first analyze the Ising model with frustrated plaquettes. We use an algebraic approach to derive the result that an Ising model with…
A class of two-dimensional globally scale-invariant, but not conformally invariant, theories is obtained. These systems are identified in the process of discussing global and local scaling properties of models related by duality…
We have provided a concise introduction to the Ising model as one of the most important models in statistical mechanics and in studying the phenomenon of phase transition. The required theoretical background and derivation of the…
We discuss two athermal types of dynamics suitable for spin-models designed to model repeated tapping of a granular assembly. These dynamics are applied to a range of models characterised by a 3-spin Hamiltonian aiming to capture the…
Models which allow an explicit application to structurally modulated substances are reviewed within the frame of a symmetry-based approach starting from discrete lattice theory. Focus is set on models formulated in terms of local variables…
In this paper we study the phase diagram of two Ising planes coupled by a standard spin-spin interaction with bond randomness in each plane. The whole phase diagram is analyzed by help of Monte Carlo simulations and field theory arguments.
We rigorously prove the existence and the conformal invariance of scaling limits of the magnetization and multi-point spin correlations in the critical Ising model on arbitrary simply connected planar domains. This solves a number of…
Among the topics we discuss are certain joint densities (for sides and for angles), acuteness probabilities and bivariate Rice moments.
Classical spin models with discrete or continuous degrees of freedom arise in many studies of complex physical systems. A wide class of hard real-life optimisation problems can be formulated as a minimisation of a spin Hamiltonian. Here we…
The notion of modular covariance is reviewed and the reconstruction of the Poincar\'e group extended to the low-dimensional case. The relations with the PCT symmetry and the Spin and Statistics theorem are described.
I present an overview of the standard model, concentrating on its global continuous symmetries, both exact and approximate. There are four lectures, dedicated to spacetime symmetry, flavor symmetry, custodial symmetry, and scale symmetry.…
We discuss several algorithms for sampling from unnormalized probability distributions in statistical physics, but using the language of statistics and machine learning. We provide a self-contained introduction to some key ideas and…
The topological hypothesis claims that phase transitions in a classical statistical mechanical system are related to changes in the topology of the level sets of the Hamiltonian. So far, the study of this hypothesis has been restricted to…