Groundstate threshold pc in Ising frustration systems on 2D regular lattices

Abstract

Abstract In 2D Ising± J models on square as well as regular triangular and honeycomb lattices the groundstate threshold p c between ferro- and paramagnetism is determined by means of simulations of exact groundstates on L × L lattices up to a size of L = 300. To this end minimal matchings of frustrated plaquettes are formed following an approach proposed by Toulouse. Thus we obtain p c,hc ≈0.06, p c,sq ≈0.10, p c,tr ≈0.15. Moreover, investigating the so-called adjoined problem we locate p c,type near the concentration π type where a certain rational function ρ type ( p ) takes its minimum. In particular π sq =0.100…,π hc =0.061…, π tr = 0.150…. There is the conjecture that p c,type = π type .