Combinatorial Problems in Ferromagnetic Models

• Grant number: 14/10637-9
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: August 01, 2014
• End date: July 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Rodrigo Bissacot Proença
• Grantee: Eric Ossami Endo
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 11/16265-8 - Low dimensional dynamics, AP.TEM
• Associated scholarship(s): 15/14434-8 - Phase Transitions in Spin Models with General External Fields, BE.EP.DR

Abstract

One of the central problems in Statistical Mechanics is the question of when a model has a phase transition. Being the Ising model the most revisited and best understood theory model is natural to expect that variations on this theme are also well understood. The objective of this project is, among other things, investigate the possibility of a full characterization of the fields that allow or not the phase transition in the ferromagnetic Ising model. This would complete the study which started in previous work by making certain assumptions about the behavior of the field has been proved the existence or absence of the phenomenon for certain classes of models type ising not necessarily uniform fields.

Scientific publications

(6)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BISSACOT, RODRIGO; ENDO, ERIC O.; VAN ENTER, AERNOUT C. D.; KIMURA, BRUNO; RUSZEL, WIOLETTA M.. Contour Methods for Long-Range Ising Models: Weakening Nearest-Neighbor Interactions and Adding Decaying Fields. ANNALES HENRI POINCARE, v. 19, n. 8, p. 2557-2574, AUG 2018. (16/08518-7, 15/14434-8, 16/25053-8, 14/10637-9)

BISSACOT, RODRIGO; ENDO, ERIC OSSAMI; VAN ENTER, AERNOUT C. D.. Stability of the phase transition of critical-field Ising model on Cayley trees under inhomogeneous external fields. Stochastic Processes and their Applications, v. 127, n. 12, p. 4126-4138, DEC 2017. (16/08518-7, 11/16265-8, 15/14434-8, 14/10637-9)

ENDO, ERIC O.; VALESIN, DANIEL. Local limits of spatial Gibbs random graphs. ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, v. 17, n. 1, p. 51-63, 2020. (15/14434-8, 14/10637-9)

ALON, NOGA; BISSACOT, RODRIGO; ENDO, ERIC OSSAMI. Counting contours on trees. LETTERS IN MATHEMATICAL PHYSICS, v. 107, n. 5, p. 887-899, MAY 2017. (11/16265-8, 14/10637-9, 16/08518-7, 15/14434-8)

BISSACOT, RODRIGO; ENDO, ERIC O.; VAN ENTER, AERNOUT C. D.; LE NY, ARNAUD. Entropic Repulsion and Lack of the g-Measure Property for Dyson Models. Communications in Mathematical Physics, v. 363, n. 3, p. 767-788, NOV 2018. (15/14434-8, 16/25053-8, 14/10637-9, 16/08518-7, 11/16265-8)

BISSACOT, RODRIGO; ENDO, ERIC O.; VAN ENTER, AERNOUT C. D.; KIMURA, BRUNO; LE NY, ARNAUD; RUSZEL, WIOLETTA M.; SIDORAVICIUS, V. Dyson Models Under Renormalization and in Weak Fields. SOJOURNS IN PROBABILITY THEORY AND STATISTICAL PHYSICS - I: SPIN GLASSES AND STATISTICAL MECHANICS, A FESTSCHRIFT FOR CHARLES M. NEWMAN, v. 298, p. 15-pg., 2019-01-01. (14/10637-9, 11/16265-8, 15/14434-8)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

ENDO, Eric Ossami. Gibbs Measures for Models on Lines and Trees. 2018. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.