Monte Carlo study of chiral criticality—XY and Heisenberg stacked-triangular antiferromagnets

H Kawamura - Journal of the Physical Society of Japan, 1992 - jstage.jst.go.jp
Journal of the Physical Society of Japan, 1992jstage.jst.go.jp
The results of extensive Monte Carlo simulations are reported on XY and Heisenberg
antiferromagnets on ad= 3-dimensional stacked-triangular lattice, which are expected to
belong to the recently identined n= 2 and 3 chiral universality classes, respectively. The
lattices studied consist ofL3+ spins with 18-<-LE {60. The study is an extension of earlier
Monte Carlo simulations for the same system with smaller lattices. A continuous transition
characterized by the novel critical exponents is found with a== O. 34Å} O. 06, 6= O. 253Å} O …
The results of extensive Monte Carlo simulations are reported on XY and Heisenberg antiferromagnets on ad= 3-dimensional stacked-triangular lattice, which are expected to belong to the recently identined n= 2 and 3 chiral universality classes, respectively. The lattices studied consist ofL3+ spins with 18-<-LE {60. The study is an extension of earlier Monte Carlo simulations for the same system with smaller lattices. A continuous transition characterized by the novel critical exponents is found with a== O. 34Å} O. 06, 6= O. 253Å} O. Ol, 7== 1.13 Å} O. 05 and v= O. 54Å} O. 02 for the XY (n= 2) case, and with a= O. 24Å} O. 08, 6= O. 30Å} O. 02, 7== 1.17 Å} O. 07 and v= O. 59Å} O. 02 for the Heisenberg (n== 3) case. The specinc-heat amplitude ratio is esti-mated to beA'/A--= O. 36Å} O. 2 and A'/A-= O. 54Å} O. 2 in the n= 2 and n== 3 cases, respectively. The nature of the chiral ordering is also studied, and various chirality ex-ponents are determined. The results are discussed in conjunction with the recent renormalization-group calculations and experiments. gl. Introduction
Several years ago, the author pointed out on the basis of a symmetry argument and Monte Carlo simulations that frustrated vector antiferromagnets on ad= 3-dimensional stacked-triangular (or simple hexagonal) lat-tice exhibited unusual critical behavior which seemed to lie in a new universality class distinct, from the conventional 0 (n) Heisenberg universality class. i'2) Indeed, Monte Carlo estimates of various critical exponents of XY and Heisenberg stacked-triangular antiferromagnets diEered signihcantly from the conventional XY (n= 2) and Heisenberg (n= 3) values. The values reported in ref. 2, for example, were (N= O. 4Å} O. 1, 6= O. 25Å} O. 02, 7= 1.1 Å} O. 1, v== O. 53Å} O. 03 for n=: 2, and a= O. 34Å} O. 1, 6= O. 28Å} O. 02, 7= 1.1 Å} O. 1, v== O. 55Å} O. 03 for n== 3, respectively, which should be compared with the conventional exponent values, a== O. 1---O. 1, 6== O. 33--O. 37, 7= 1.24--1.39 and v= O. 63--O. 70. Theoretical studies based on the renormalization-group (RG) e=: 4--d expansion, 3) 1/n expansion, 3) and s: d-2 ex-pansion) have revealed that such novel critical behavior is most probably caused by a new
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