Response of Fully-Frustrated Ising Square Lattice to a Type of Symmetry Breaking Field

Abstract

219The fully-frustrated Ising system without the frozen spin state shows the diverging behavior with the critical index 8=3 in the response to a replica type·of field at low temperature. The replica field provides a relevant external field for a specific Villain-Stephenson universality class treated recently by Horiguchi, Tanaka and Morita.' § 1. IntroductionFor typical 2D strongly-frustrated Ising lattices, it is rigorously proved that the phase is paramagnetic ~t any finite temperature.1H ) That is, there exists no symmetry broken state and thermodynamic functions are invariant for all the spin inversion. On the other hand, the pair spin correlation function at OK exhibits a long-ranged algebraic decay2),3) and it is expected that some physical quantities show anomalous behavior near OK. In fact, we can find an external field which enhances those spin configurations induced preferably by the frustrated interaction. More concretely, we can provide a conjugate external field of frustrated spin configurations by an excellent device called real replica method. Originally, the reall-eplica method is invented by Suzuki 4 ),5) and developed by Suzuki and Miyashita 6 ) to detect the spin glass order. The essential point is that the best reference of an order in an Ising lattice, if it exists in some sense, is the identical lattice. We can regard the replicated lattice as the conjugate field of order. The response of a 2D frustrated lattice to the replica field is investigated by simulation. The data show a type of response diverging behavioe) with the exponent 0'=3. Scaling analysis supports the result. We try to interpret this behavior as an indication of ordered state even for the 2D fully-frustrated lattices.In § 2, the replica method is reformulated. In § 3, for the fully-frustrated square lattice, the simulation is performed to obtain the response to the replica field, i. e., the conjugate magnetization and susceptibility. In § 4, a scaling interpretation for the response is presented, and in § 5 concluding remarks are made. § 2. Replica field We prepare two layers or replicas of Ising Lx L square lattice with an appropriate fully-frustrated arrangement of exchange integrals J ij between i-th and j-th sites (each of them takes + J or -n. We assign additional exchange integrals Jz between all the pair of corresponding spins on two replicas. Designate the spin value of i-th site on the first replica as S/1) and that on the second one as SpY. Then, the Hamiltonian H of this replicated lattice can be written as