Statistical Mechanics Invited Talk

Youjin Deng (Uni. of Sci. & Tech. of China, Hefei)

Universal amplitudes in the canonical ensemble

Universal amplitudes play an important role in the numerical study of critical phenomena. We study the finite-size scaling of universal amplitudes in the q-state random-cluster model under the constraint that the total number of occupied bonds is fixed, so that the canonical ensemble applies. We observe that at criticality, new finite-size corrections with exponent ycan=-|2yt-d| are induced, where yt=1/ν is the thermal renormalization exponent and d is the spatial dimension. Moreover, we find that universal values of dimensionless parameters like Binder ratios and wrapping probabilities are modified for systems with 2yt-d>0. For the bond percolation model where thermal fluctuations are absent, the correction exponent ycan still occurs, and universal amplitudes like the excess cluster number are not only modified but become non-universal. A full explanation should take into account fluctuation-suppression effects, in addition to the well-known Fisher renormalization mechanism.

Reference: J. Phys. A: Math. Theor. 45, 494006 (2012)