We study the antiferromagnetic Potts model on the Poissonian Erdős-Rényi random graph. By identifying a suitable interpolation structure and an extended variational principle, together with a positive temperature second-moment analysis we prove the existence of a phase transition at a positive critical temperature. Upper and lower bounds on the temperature critical value are obtained from the stability analysis of the replica symmetric solution (recovered in the framework of Derrida-Ruelle probability cascades) and from an entropy positivity argument.
Antiferromagnetic Potts Model on the Erdős-Rényi Random Graph / Pierluigi Contucci; Sander Dommers; Cristian Giardina; Shannon Starr. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - STAMPA. - 323:2(2013), pp. 517-554. [10.1007/s00220-013-1778-y]
Antiferromagnetic Potts Model on the Erdős-Rényi Random Graph
CONTUCCI, PIERLUIGI;
2013
Abstract
We study the antiferromagnetic Potts model on the Poissonian Erdős-Rényi random graph. By identifying a suitable interpolation structure and an extended variational principle, together with a positive temperature second-moment analysis we prove the existence of a phase transition at a positive critical temperature. Upper and lower bounds on the temperature critical value are obtained from the stability analysis of the replica symmetric solution (recovered in the framework of Derrida-Ruelle probability cascades) and from an entropy positivity argument.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
