AN EXTENDED CONCEPT OF UNIVERSALITY IN A STATISTICAL MECHANICS MODEL
Carlos Wexler, Cintia Mariela Lapilli, Peter Pfeifer
Nature uses phase transitions as powerful regulators of processes ranging from climate to the alteration of phase behavior of cell membranes, building on the fact that thermodynamic properties of a solid, liquid, or gas are sensitive fingerprints of intermolecular interactions. The only known exceptions from this sensitivity are critical points, where two phases become indistinguishable and thermodynamic properties exhibit universal behavior: systems with widely different intermolecular interactions behave identically. Here we report a new, stronger form of universality, in which different members of a family of two-dimensional systems—the discrete p-state clock model—behave identically both near and away from critical points, if the temperature exceeds a value Teu ('extended universality). We show that all thermal averages are identical to those of the continuous planar rotor model (p = ∞) above Teu, that phase transitions above Teu are identical to the Berezinskii-Kosterlita-Thouless (BKT) transition, and that transitions below Teu are distinctly non-BKT. The results generate a comprehensive map of the three phases of the model and, by virtue of the discrete rotors behaving like continuous rotors, an emergent symmetry, not present in the Hamiltonian. This symmetry, or many-to-one map of intermolecular interactions onto thermodynamic states, demonstrates previously unknown limits for macroscopic distinguishability of different microscopic interactions.
International Journal of Modern Physics B•Dec 15, 2006•0 citations