Precursor phenomena in frustrated systems

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 59, Issue 6, 1999, Pages 6409-6412

  Franzese, Giancarlo ^a,b,c   Coniglio, Antonio ^a,b,c,d  

^a ROMA TRE UNIVERSITY   (Italy)

^b UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^c INFM   (Italy)

^d INFN SEZIONE DI NAPOLI   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE;

EID: 0000698943     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.59.6409     Document Type: Article

References (28)

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11. (Formula presented) is defined as the highest ordering temperature allowed by the distribution of interactions.
12. C. M. Fortuin and P. W. Kasteleyn, Physica (Amsterdam) 57, 536 (1972)
13. A. Coniglio and W. Klein, J. Phys. A 13, 2775 (1980).
14. FF spin systems on lattices are such that every elementary cell of the lattice has an odd number of antiferromagnetic interactions; see J. Villain, J. Phys. C 10, 1717 (1977).
15. A. Fierro, G. Franzese, A. de Candia, and A. Coniglio, Phys. Rev. E 59, 60 (1999).
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19. F. di Liberto and F. Peruggi, Physica A 248, 273 (1998).
20. G. Franzese (unpublished).
21. For noninteger s the Hamiltonian in Eq. (1) is not defined, but its partition function, written in a percolation approach [A. Coniglio, F. di Liberto, G. Monroy, and F. Peruggi, Phys. Rev. B 44, 12 605 (1991)], is well defined for every value of s. In this sense one can consider s as a continuous variable and the (Formula presented) case as the limiting case for the (Formula presented) cases 14.
22. Data are averaged over a number of random interaction configurations (Formula presented). For each temperature and each interaction configuration, after (Formula presented) MC steps (defined as the update of the whole system) of equilibration, we have recorded the data for a number of MC steps that goes from (Formula presented) for (Formula presented) to (Formula presented) for (Formula presented), always with (Formula presented), using an annealing procedure, i.e., with a slow cooling of the system at each temperature. To verify that the statistics is sufficient for the considered temperatures, we compared the data obtained starting from a random configuration with those obtained from the annealing method, observing the same results.
23. The integral correlation time is defined as (Formula presented).
24. In the case (c) it is possible to do fits with only two free parameters, fitting linearly the short time behavior (described by (Formula presented) and (Formula presented) and separately the long time behavior (described by (Formula presented) and (Formula presented) with (Formula presented) and x fixed.
25. In 2D, (Formula presented) with (Formula presented) 16 while (Formula presented) 14, therefore (Formula presented) increases with s.
26. The same qualitative results are seen for (Formula presented) and x fit parameters associated to autocorrelation functions of the Potts magnetization, while for this critical quantity the (Formula presented) exponent diverges near the transition temperature (Formula presented)
27. G. Fromzese and A. Coniglio (unpublished).
28. L. Andreozzi, M. Giorolono, and D. Leporini, J. Non-Cryst. Solids 235–237, 219 (1998).