Universal Ising dynamics in two dimensions

被引:17
作者
Nightingale, MP
Blote, HWJ
机构
[1] Univ Rhode Isl, Dept Phys, Kingston, RI 02881 USA
[2] Tech Univ Delft, Fac Tech Nat Kunde, NL-2600 GA Delft, Netherlands
来源
PHYSICA A | 1998年 / 251卷 / 1-2期
基金
美国国家卫生研究院; 美国国家科学基金会;
关键词
critical dynamics; universality; Ising models;
D O I
10.1016/S0378-4371(97)00605-5
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We explore several dominant eigenvalues of the spectra of Markov matrices governing the dynamics of models in the universality class of the two-dimensional Ising model. By means of a variational approximation, we determine autocorrelation times of progressively rapid relaxation modes. The approximation of one eigenstate, associated with the slowest mode, is employed in a variance-reducing Monte-Carlo method. The resulting correlation times, for which statistical errors exceed the systematic errors associated with the variational approximation, are used for a finite-size scaling analysis which corroborates universality of the dynamic critical exponent z for three distinct Ising models on the square lattice. Tentative, variational results for subdominant states strongly suggest that the amplitudes of the divergent time scales associated with different relaxation modes differ solely by metric factors, setting a single non-universal time scale for each model. A by-product of our analysis is a highly accurate confirmation of static universality. (C) 1998 Elsevier Science B.V. All rights reserved.
引用
收藏
页码:211 / 223
页数:13
相关论文
共 20 条
[1]   THE CALCULATION OF EXCITED-STATES WITH QUANTUM MONTE-CARLO .2. VIBRATIONAL EXCITED-STATES [J].
BERNU, B ;
CEPERLEY, DM ;
LESTER, WA .
JOURNAL OF CHEMICAL PHYSICS, 1990, 93 (01) :552-561
[2]   UNIVERSALITY IN TWO-DIMENSIONAL ISING-MODELS [J].
BLOTE, HWJ ;
NIGHTINGALE, MP .
PHYSICA A, 1985, 134 (01) :274-282
[3]   QUANTUM MONTE-CARLO FOR FLOPPY MOLECULES - VIBRATIONAL-STATES OF C-3 [J].
BROWN, WR ;
GLAUSER, WA ;
LESTER, WA .
JOURNAL OF CHEMICAL PHYSICS, 1995, 103 (22) :9721-9725
[4]  
CARDY J, 1987, PHASE TRANSITIONS CR, V11
[5]   CONFORMAL-INVARIANCE AND UNIVERSALITY IN FINITE-SIZE SCALING [J].
CARDY, JL .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1984, 17 (07) :L385-L387
[6]   THE CALCULATION OF EXCITED-STATE PROPERTIES WITH QUANTUM MONTE-CARLO [J].
CEPERLEY, DM ;
BERNU, B .
JOURNAL OF CHEMICAL PHYSICS, 1988, 89 (10) :6316-6328
[7]   TIME-DEPENDENT STATISTICS OF ISING MODEL [J].
GLAUBER, RJ .
JOURNAL OF MATHEMATICAL PHYSICS, 1963, 4 (02) :294-&
[8]  
KAWASAKI K, 1972, PHASE TRANSITIONS CR, V2
[9]  
NIEMEIJER T, 1971, PHASE TRANSITIONS CR, V6
[10]  
Nightingale M. P., 1976, Physica A, V83A, P561