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Apparent phase transitions in finite one-dimensional sine-Gordon lattices Saul Ares,* Jose A. Cuesta,

Summary: Apparent phase transitions in finite one-dimensional sine-Gordon lattices
Sau´l Ares,* Jose´ A. Cuesta,
and Angel Sa´nchez
Grupo Interdisciplinar de Sistemas Complejos (GISC) and Departamento de Matema´ticas, Universidad Carlos III de Madrid,
Avenida de la Universidad 30, 28911 Legane´s, Madrid, Spain§
Rau´l Toral
Institut Mediterrani d'Estudis Avanc¸ats (IMEDEA), CSIC-Universitat de les Illes Balears,
Campus UIB, 07071 Palma de Mallorca, Spain¶
Received 15 November 2002; published 17 April 2003
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.
Sa´nchez, 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.
DOI: 10.1103/PhysRevE.67.046108 PACS number s : 05.70.Fh, 05.10. a, 68.35.Ct, 64.60.Cn
More than 50 years ago, van Hove 1 proved that true
thermodynamic phase transitions, defined as singularities of
the free energy, could not occur in a class of one-dimensional


Source: Ares, Saúl - Max-Planck-Institut für Physik komplexer Systeme
Cuesta, José A. - Departamento de Matemáticas, Universidad Carlos III de Madrid
Sánchez, Angel "Anxo" - Departamento de Matemáticas, Universidad Carlos III de Madrid
Toral, Raúl - Mediterranean Institute for Advanced Studies & Departament de Física, Universitat de les Illes Balears


Collections: Biology and Medicine; Materials Science; Mathematics; Physics