Ares S, Cuesta JA, Sánchez A, Toral R. Apparent phase transitions in finite one-dimensional sine-Gordon lattices.
PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003;
67:046108. [PMID:
12786437 DOI:
10.1103/physreve.67.046108]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2002] [Indexed: 05/24/2023]
Abstract
We study the one-dimensional sine-Gordon model as a prototype of roughening phenomena. In spite of the fact that it has been recently proven that this model cannot have any phase transition [J. A. Cuesta and A. Sánchez, J. Phys. A 35, 2373 (2002)], Langevin as well as Monte Carlo simulations strongly suggest the existence of a finite temperature separating a flat from a rough phase. We explain this result by means of the transfer operator formalism and show as a consequence that sine-Gordon lattices of any practically achievable size will exhibit this apparent phase transition at unexpectedly large temperatures.
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