The critical ensemble: An efficient simulation of a macroscopic system at the critical point

N.G. Antoniou, F.K. Diakonos, E.N. Saridakis and G.A. Tsolias

Physica A: Statistical Mechanics and its Applications, 2007, vol. 376, issue C, 308-318

Abstract: It is well known that conventional simulation algorithms are inefficient for the statistical description of macroscopic systems exactly at the critical point due to the divergence of the corresponding relaxation time (critical slowing down). On the other hand the dynamics in the order parameter space is simplified significantly in this case due to the onset of self-similarity in the associated fluctuation patterns. As a consequence the effective action at the critical point obtains a very simple form. In the present work we show that this simplified action can be used in order to simulate efficiently the statistical properties of a macroscopic system exactly at the critical point. Using the proposed algorithm we generate an ensemble of configurations resembling the characteristic fractal geometry of the critical system related to the self-similar order parameter fluctuations. As an example we simulate the one-component real scalar field theory at the transition point T=Tc as a representative system belonging to the 3-D Ising universality class.

Keywords: Critical point; Order parameter fluctuations; Fractal clusters; Effective action; Monte-Carlo simulation (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:376:y:2007:i:c:p:308-318

DOI: 10.1016/j.physa.2006.10.043

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