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Physical review. B, Condensed matter

Transient theory for Monte Carlo renormalization with application to the pure two-dimensional Ising model

J. Eckert, M. Fähnle

Published Dec 1, 1993• 0 citations
Publisher

Abstract

Taking into account quadratic corrections to the linearized renormalization transformation, a simple expression for the transient behavior of the local eigenvalues obtained from a Monte Carlo renormalization-group (MCRG) analysis is derived, which constitutes a basis for extrapolation procedures commonly used in MCRG calculations. The method is applied to investigate the effect of irrelevant and relevant scaling fields for the d=2 Ising model. It is shown that the transient effect for the magnetic eigenvalue is very fast because it is dominated not by the largest, but by the second largest irrelevant scaling exponent. Peculiarities observed for the effect of the relevant thermal scaling field \ensuremath{\tau}=${\mathit{a}}_{\ifmmode\pm\else\textpm\fi{}}$(T-${\mathit{T}}_{\mathit{c}}$)/${\mathit{T}}_{\mathit{c}}$ may be interpreted by assuming ${\mathit{a}}_{+}$\ensuremath{\ne}${\mathit{a}}_{\mathrm{\ensuremath{-}}}$, i.e., a nonanalytic scaling field.

DOI
10.1103/physrevb.48.16099

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