We examine zero-temperature hysteresis in random-field XY and Heisenberg models in the zero-frequency limit of a cyclic driving field. Exact expressions for hysteresis loops are obtained in the mean-field approximation. These show rather unusual features. We also perform simulations of the two models on a simple-cubic lattice and compare them with the predictions of the mean-field theory.

AbslracL The study by kinetic mean-field techniques of a ddimensional king system characterized by a sort of dpomicol &order reveals a rich phase diagram which exhibils a non-equilibrium lricnlical paint (only) for d > 2, and re-entrance phenomena. The system time evolution is stochastic due to the simultaneous action of wera l independent spin-flip mechanisms, each cot’responding to a differen...

Motivated by Segal’s axiom of conformal field theory, we do a survey on geometrical random fields. We do a history of continuous random fields in order to arrive at a field theoretical analog of Klauder’s quantization in Hamiltonian quantum mechanic by using infinite dimensional Airault-Malliavin Brownian motion. AMS 2000 subject classifications: Primary 60G60; secondary 81T40.

In this article, we propose a generalization of the theory of diffusion approximation for random ODE to a nonlinear system of random Schrödinger equations. This system arises in the study of pulse propagation in randomly birefringent optical fibers. We first show existence and uniqueness of solutions for the random PDE and the limiting equation. We follow the work of Garnier-Marty [16, 20], whe...

This paper explores the connection between belief inference and game-theoretic equilibria within the context of graphical models. While a lot of the work in graphical models for game theory has mirrored that in probabilistic graphical models, the paper also considers the opposite direction: Taking advantage of recent advances in equilibrium computation for probabilistic inference. In particular...

We show that if a complexity class C is closed downward under polynomialtime majority truth-table reductions (≤pmtt), then practically every other “polynomial” closure property it enjoys is inherited by the corresponding bounded 2-sided error class BP[C]. For instance, the Arthur-Merlin game class AM [Bab85] enjoys practically every closure property of NP. Our main lemma shows that for any rela...