Tests of Conformal Invariance in Randomness Induced Second-Order Phase Transitions

Details Tests of Conformal Invariance in Randomness Induced Second-Order Phase Transitions Tests of Conformal Invariance in Randomness Induced Second-Order Phase Transitions

1998-10-21

arxiv.org/abs/cond-mat/9810270v2

Phys. Rev. E 58 (1998) R6899-R6902

Physics

Condensed Matter

Statistical Mechanics

LaTeX file with Revtex, 4 pages, 4 eps figures, to appear in Phys. Rev. E, minor corrections

Scientific paper

10.1103/PhysRevE.58.R6899

The conformal covariance of correlation functions is checked in the second-order transition induced by random bonds in the two-dimensional 8-state Potts model. The decay of correlations is obtained {\it via} transfer matrix calculations in a cylinder geometry, and large-scale Monte Carlo simulations give access to the correlations and the profiles inside a square with free or fixed boundary conditions, respectively. In both geometries, conformal transformations constrain the form of the spatial dependence, leading to accurate determinations of the order parameter scaling index in good agreement with previous independent determinations obtained through standard techniques. The energy density exponent is also computed.

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