Large deviations and continuum limit in the 2D Ising model

A Continuum Generalization of the Ising Model

The Lenz-Ising model has served for almost a century as a basis for understanding ferromagnetism, and has become a paradigmatic model for phase transitions in statistical mechanics. While retaining the Ising energy arguments, we use techniques previously applied to sociophysics to propose a continuum model. Our formulation results in an integro-differential equation that has several advantages ...

The Nature of the Continuum Limit in the 2D RP^2 Gauge Model

The RP 2 gauge model which allows interpolation between the RP 2 and O(3) spin models is studied in 2D. We use Monte-Carlo renormalization techniques for blocking the mean spin-spin interaction, 〈A〉, and the mean gauge field plaquette, 〈P 〉. The presence of the O(3) renormalized trajectory is verified and is consistent with the known three-loop β-function. The first-order ‘vorticity’ transition...

Multivariate Large Deviations with Stable Limit Laws

The large deviation problem for sums of i.i.d. random vectors is considered. It is assumed that the underlying distribution is absolutely continuous and its density is of regular variation. An asymptotic expression for the probability of large deviations is established in the case of a non-normal stable limit law. The role of the maximal summand is also emphasized. AMS Subject Classification: P...

The solution of the 2D Ising model

Large deviations from the thermodynamic limit in globally coupled maps

Systems of a large number N of globally coupled maps have become popular as a relatively simple prototype of high-dimensional dynamics, showing many interesting and typical phenomena like synchronisation, cluster formation and multistability, and having potential applications in systems like Josephson junction arrays or in biophysical models. There exists a wealth of numerical investigations of...