Renormalization-group at criticality and complete analyticity of constrained models: a numerical study

Дата и время публикации : 1996-03-14T17:01:48Z

Авторы публикации и институты :
Emilio N. M. Cirillo
E. Olivieri

Ссылка на журнал-издание: Journ. Stat. Phys. 86, (1997)
Коментарии к cтатье: 39 pages, teX file, 4 Postscript figures, 1 TeX figure
Первичная категория: hep-th

Все категории : hep-th, cond-mat

Краткий обзор статьи: We study the majority rule transformation applied to the Gibbs measure for the 2–D Ising model at the critical point. The aim is to show that the renormalized hamiltonian is well defined in the sense that the renormalized measure is Gibbsian. We analyze the validity of Dobrushin-Shlosman Uniqueness (DSU) finite-size condition for the "constrained models" corresponding to different configurations of the "image" system. It is known that DSU implies, in our 2–D case, complete analyticity from which, as it has been recently shown by Haller and Kennedy, Gibbsianness follows. We introduce a Monte Carlo algorithm to compute an upper bound to Vasserstein distance (appearing in DSU) between finite volume Gibbs measures with different boundary conditions. We get strong numerical evidence that indeed DSU condition is verified for a large enough volume $V$ for all constrained models.

Category: Physics