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Convergence and extrapolation in finite-size scaling renormalization

Vladimir Privman A

Physica A Statistical Mechanics and its ApplicationsFeb 1, 198453 citations

Convergence of finite size scaling analysis: Weak size dependence of renormalization transformations

Mirosław R. Dudek, J. M. J. van Leeuwen, Henk W. J. Blöte

Physica A Statistical Mechanics and its ApplicationsNov 1, 19876 citations

Finite-size scaling and the renormalization group

Joseph Rudnick, Hong Min Guo, David Jasnow

Journal of Statistical PhysicsNov 1, 1985157 citations

Convergence of finite-size scaling renormalisation techniques

Vladimir Privman A, Michael Ellis Fisher

The rate of convergence of the transfer matrix finite-size scaling (or phenomenological renormalisation) method is studied. It is shown both heuristically and numerically that the convergence of estimates for exponents, etc. is governed asymptotically by the leading irrelevant-variable scaling exponent. The more rapid apparent convergence rates observed in many practical calculations for two-dimensional lattices of widths up to ten lattice spacings are attributed to cancellation between various correction terms.The rate of convergence of the transfer matrix finite-size scaling (or phenomenological renormalisation) method is studied. It is shown both heuristically and numerically that the convergence of estimates for exponents, etc. is governed asymptotically by the leading irrelevant-variable scaling exponent. The more rapid apparent convergence rates observed in many practical calculations for two-dimensional lattices of widths up to ten lattice spacings are attributed to cancellation between various correction terms.

Journal of Physics A Mathematical and GeneralJun 21, 198385 citations

Renormalisation group treatment of finite size scaling with ε expansion

A. M. Nemirovsky, Karl F. Freed

The use of renormalisation group techniques away from the critical point is shown to enable the calculation of finite size scaling corrections to scaling functions with epsilon -expansion methods. The authors consider the N-vector phi 4 theory for a layered geometry with periodic boundary conditions and evaluate the correlation function, susceptibility, correlation lengths and shift in the critical temperature to order epsilon .

Journal of Physics A Mathematical and GeneralApr 21, 198523 citations

Finite-Size Scaling and the Renormalization Group

Joseph Rudnick, Hong Mei Guo, David Jasnow

Current physics sources and commentsJan 1, 19882 citations

Convergence of Finite-Size Scaling Renormalisation Techniques

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