1997/10/10 by Paul J. M. Bastiaansen, Hubert J. F. Knops, H. J. F. Knops · 1 citation
Mathematics · Physics and Astronomy · #Quantum many-body systems #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.57.3784
published as Phys.Rev. E57 (1998) 3784-3796 · 18 pages REVTeX, 4 postscript figures included
arxiv created 1997/10/10 · openalex publication_date 1998/04/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We present a finite size scaling technique to calculate the central charge and some critical exponents of two-dimensional critical models with a Monte Carlo simulation. We use systems with dimensions L\ifmmode×\else\texttimes\fiM, and focus on the scaling behavior in M/L. The finite size scaling relation that we use is the universal expression for the stress tensor on the torus. The stress tensor is the operator that governs the anisotropy of the system, and stems for the theory of conformal invariance. We show that a lattice representation of the stress tensor can easily be constructed, such that its expectation value on the torus can be calculated in a Monte Carlo simulation. In doing so, we observe that the stress tensor turns out to be remarkably insensitive to critical slowing down. We show that the typical simulation time scales with the linear system dimension L roughly as L4, and that this scaling holds for the ordinary Metropolis algorithm as well as for more sophisticated cluster algorithms, such that it is fruitless to invoke the latter. We test the method for the Ising model (with central charge c=(1)/(2)), the Ashkin-Teller model (c=1), and the F model (also c=1).