Publicación: LACK OF PHASE TRANSITIONS IN STAGGERED MAGNETIC SYSTEMS. A COMPARISON OF UNIQUENESS CRITERIA
Fecha
2021
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JOURNAL OF MATHEMATICAL PHYSICS
Resumen
WE STUDY A FERROMAGNETIC ISING MODEL WITH A STAGGERED CELL-BOARD MAGNETIC FIELD PREVIOUSLY PROPOSED FOR IMAGE PROCESSING [MARUANI ET AL., MARKOV PROCESSES RELAT. FIELDS 1, 419?442 (1995)]. WE COMPLEMENT PREVIOUS RESULTS ON THE EXISTENCE OF PHASE TRANSITIONS AT LOW TEMPERATURE [GONZÁLEZ-NAVARRETE ET AL., J. STAT. PHYS. 162, 139?161 (2016)] BY DETERMINING BOUNDS TO THE REGION OF UNIQUENESS OF GIBBS MEASURES. WE ESTABLISH SUFFICIENT RIGOROUS UNIQUENESS CONDITIONS DERIVED FROM THREE DIFFERENT CRITERIA: (1) DOBRUSHIN CRITERION [R. DOBRUSHIN, THEORY PROBAB. APPL. 13, 197?224 (1968)], (2) DISAGREEMENT PERCOLATION [J. VAN DEN BERG AND C. MAES, ANN. PROBAB. 22, 749?763 (1994)], AND (3) DOBRUSHIN?SHLOSMAN CRITERIA [R. DOBRUSHIN AND S. SHLOSMAN, IN STATISTICAL PHYSICS AND DYNAMICAL SYSTEMS: RIGOROUS RESULTS, EDITED BY J. FRITZ, A. JAFFE, AND D. SZASZ (BIRKHAUSER, BASEL, 1985)]. THESE CONDITIONS ARE SUBSEQUENTLY SOLVED NUMERICALLY AND THE RESULTING UNIQUENESS REGIONS ARE COMPARED.
