Physics (Internal)

Phase transitions in the frustrated Ising model on the square lattice

This event is part of the Condensed Matter Theory Seminar Series.

Abstract:

The ferromagnetic Ising model (with coupling J1) on the square lattice
plays an important role in the study of phase transitions as it is one of
the few models in d>1 that admits an exact solution. Adding a next-nearest
neighbor antiferromagnetic interaction (J2) leads to frustration in the
system. The phase transitions in this model have been investigated
analytically and numerically for several years now but these are still not
well understood. In this talk, I will discuss some ongoing work in which we
show that when J2/J1>0.5, this model has a line of very weak first-order
phase transitions that terminates at J2 approx. 0.7J1, where the
multicritical point is likely to be in the same universality as the q=4
Potts model. Beyond J2 approx 0.7J1, the transition is continuous and in the Ashkin-Teller (AT) universality class with continuously varying exponents. We also show that the q=4 Potts model and transitions in its neighborhood on the AT line exhibit pseudo first-order behavior in finite systems even though the transitions are continuous in the infinite size limit.

(in collaboration with Songbo Jin and Anders W. Sandvik)