Premium
Numerical tests of conjectures of conformal field theory for three‐dimensional systems
Author(s) -
Weigel Martin,
Janke Wolfhard
Publication year - 1998
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/(sici)1521-3889(199811)7:5/6<575::aid-andp575>3.0.co;2-m
Subject(s) - scaling , ising model , conformal map , conformal field theory , monte carlo method , boundary value problem , physics , observable , statistical physics , critical phenomena , boundary (topology) , periodic boundary conditions , mathematics , mathematical analysis , phase transition , geometry , quantum mechanics , statistics
The concept of conformal field theory provides a general classification of statistical systems on two‐dimensional geometries at the point of a continuous phase transition. Considering the finite‐size scaling of certain special observables, one thus obtains not only the critical exponents but even the corresponding amplitudes of the divergences analytically. A first numerical analysis brought up the question whether analogous results can be obtained for those systems on three‐dimensional manifolds. Using Monte Carlo simulations based on the Wolff single‐cluster update algorithm we investigate the scaling properties of O( n ) symmetric classical spin models on a three‐dimensional, hyper‐cylindrical geometry with a toroidal cross‐section considering both periodic and antiperiodic boundary conditions. Studying the correlation lengths of the Ising, the XY, and the Heisenberg model, we find strong evidence for a scaling relation analogous to the two‐dimensional case, but in contrast here for the systems with antiperiodic boundary conditions.