First- and second-order phase transitions in Potts models: Competing mechanisms (invited)

A. Nihat Berker*, David Andelman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Many condensed matter systems, ranging from adsorbed surfaces to bulk magnets, are microscopically modelled by interacting q-state Potts spins, arrayed in d dimensions. A changeover from second-order phase transitions at q≤qc(d) to first-order transitions at q≳qc can be understood as a condensation of effect vacancies, which are patches of local disorder favored by entropy. Accordingly, the renormalization-group treatment of Potts models is within context of Potts-lattice-gas models, where critical and tricritical fixed points occur at low q, but merge and annihilate at q c. This picture has led to exact tricritical exponents in two dimensions. It is also consistent with recent experimental results on intercalated systems in three dimensions. Effective vacancies in pure Potts models have also been studied by Monte Carlo simulation. Their effective chemical potential can be controlled by a four-point interaction, which proved useful in Monte Carlo renormalization-group studies.

Original languageEnglish
Pages (from-to)7923-7926
Number of pages4
JournalJournal of Applied Physics
Issue number11
StatePublished - 1982
Externally publishedYes


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