The influence of a thermodynamic constraint on the critical finite-size scaling behavior of three-dimensional Ising and XY models is analyzed by Monte-Carlo simulations. Within the Ising universality class constraints lead to Fisher renormalized critical exponents, which modify the asymptotic form of the scaling arguments of the universal finite-size scaling functions. Within the XY universality class constraints lead to very slowly decaying corrections inside the scaling arguments, which are governed by the specific heat exponent alpha. If the modification of the scaling arguments is properly taken into account in the scaling analysis of the data, finite-size scaling functions are obtained, which are independent of the constraint as anticipated by analytic theory.The influence of a thermodynamic constraint on the critical finite-size scaling behavior of three-dimensional Ising and XY models is analyzed by Monte-Carlo simulations. Within the Ising universality class constraints lead to Fisher renormalized critical exponents, which modify the asymptotic form of the scaling arguments of the universal finite-size scaling functions. Within the XY universality class constraints lead to very slowly decaying corrections inside the scaling arguments, which are governed by the specific heat exponent alpha. If the modification of the scaling arguments is properly taken into account in the scaling analysis of the data, finite-size scaling functions are obtained, which are independent of the constraint as anticipated by analytic theory.

arXiv:cond-mat/9903288Mar 18, 19991 citation

Finite-size scaling and the renormalization group

Joseph Rudnick, Hong Min Guo, David Jasnow

Journal of Statistical PhysicsNov 1, 1985157 citations

Finite-size scaling in the canonical ensemble

Youjin Deng, Henk W. J. Blöte

We investigate the critical scaling behavior of finite systems in the canonical ensemble. The essential difference with the grand canonical ensemble. i.e., the constraint on the number of particles, is already known to lead to the Fisher renormalization phenomenon that modifies the thermal critical singularities. We show that, in observables that are not Fisher renormalized, it also leads to a finite-size effect governed by an exponent $y_1$ that depends on the temperature exponent $y_t$ and the dimensionality $d$ as $y_1=-|2y_t-d|$ . We verify this prediction by a Monte Carlo analysis of several two-dimensional lattice models in the percolation, the Ising and the 3-state Potts universality classes.We investigate the critical scaling behavior of finite systems in the canonical ensemble. The essential difference with the grand canonical ensemble. i.e., the constraint on the number of particles, is already known to lead to the Fisher renormalization phenomenon that modifies the thermal critical singularities. We show that, in observables that are not Fisher renormalized, it also leads to a finite-size effect governed by an exponent $y_1$ that depends on the temperature exponent $y_t$ and the dimensionality $d$ as $y_1=-|2y_t-d|$. We verify this prediction by a Monte Carlo analysis of several two-dimensional lattice models in the percolation, the Ising and the 3-state Potts universality classes.

arXiv:cond-mat/0508348Aug 15, 20051 citation

Finite-Size Scaling and the Renormalization Group

Joseph Rudnick, Hong Mei Guo, David Jasnow

Current physics sources and commentsJan 1, 19882 citations

Ferromagnetic Phase Transition in a Heisenberg Fluid: Monte Carlo Simulations and Fisher Corrections to Scaling

I. M. Mryglod, I. P. Omelyan, R. Folk

The magnetic phase transition in a Heisenberg fluid is studied by means of the finite size scaling technique. We find that even for larger systems, considered in an ensemble with fixed density, the critical exponents show deviations from the expected lattice values similar to those obtained previously. This puzzle is clarified by proving the importance of the leading correction to the scaling that appears due to Fisher renormalization with the critical exponent equal to the absolute value of the specific heat exponent alpha. The appearance of such new corretions to scaling is a general feature of systems with constraints.The magnetic phase transition in a Heisenberg fluid is studied by means of the finite size scaling technique. We find that even for larger systems, considered in an ensemble with fixed density, the critical exponents show deviations from the expected lattice values similar to those obtained previously. This puzzle is clarified by proving the importance of the leading correction to the scaling that appears due to Fisher renormalization with the critical exponent equal to the absolute value of the specific heat exponent alpha. The appearance of such new corretions to scaling is a general feature of systems with constraints.

arXiv:cond-mat/0012110Physical Review LettersApr 2, 200128 citations

Finite-Size Scaling, Hyperscaling and the Renormalization Group

David Jasnow

WORLD SCIENTIFIC eBooksJan 1, 19902 citations

y_1

that depends on the temperature exponent

y_t

and the dimensionality

d

y_1=-|2y_t-d|

. We verify this prediction by a Monte Carlo analysis of several two-dimensional lattice models in the percolation, the Ising and the 3-state Potts universality classes.