Nonlinear Susceptibilities of the Sherrington-Kirkpatrick Model and the Spherical Model
Nonlinear Susceptibilities of the Sherrington-Kirkpatrick Model and the Spherical Model
复制标题
Sherrington-Kirkpatrick 模型和球面模型的非线性敏感性
DOI：
10.1143/ptp.64.327
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发表时间：
1980
影响因子：
--
通讯作者：
H. Takayama
中科院分区：
文献类型：
--
作者：
K. Wada;H. Takayama
自从Edward和安德森提出自旋玻璃相以来，无规竞争自旋系统一直是理论家和实验家相当关注的课题。然而，自旋玻璃（SG）转变的合作性质似乎尚未得到证实。最近，宫古等人21观察到非线性极化率的发散行为Xn = limn~o（1/（n+ 1）！）(()n+ 1 m/f）hn+ 1），（n~ 1），他们认为这是合作SG跃迁的证据。在理论上，X2在SG转变点的发散首先由Katsun 31和Suzuki唯象地预测。Suzuki 41表明，EA序参量的不稳定性导致了X2的发散，而不是X 0的发散。本文的目的是系统地分析精确可解自旋玻璃模型的非线性磁化率（NS）Xn（n = 1，2），即，Sherrington-Kirkpatrick（SK）模型71和Kosteritz等人的球形（SP）模型81。结果表明，X2在p. sc跃迁，但X ~ 2在F ~--′中正发散。P（F->SG），而P相（SG-相）中的X2总是负的。在宫古等人最近的实验中没有观察到这种转变点的符号变化。（I）SK模型中的伊辛自旋是由无限范围的、随机的相互作用耦合的，相互作用独立地分布在高斯概率密度中
Since the proposal of a spin-glass phase by Edward and Anderson (EA), 11 the random competing spin system has been the subject of considerable attension for both theoretists and experimentalists. It seems, however, that the cooperative nature of the spin glass (SG) transition has not yet been confirmed. Recently, Miyako et al. 21 have observed divergent behavior of the nonlinear susceptibilities Xn = limn~o (1/ (n+ 1) !) (()n+ 1m/f)hn+ 1), (n~ 1), which they interpret as an evidence of the cooperativeSG transition. Theoretically, the divergence of X2 at the SG transition point was predicted first by Katsura 31 and phenomenologically by Suzuki." Several theoretical investigators51 •61 have also pointed out the divergence in X2 , but not in X0 • Suzuki41 showed that the instability of the EA order parameter yields the divergence not in Xo but in X2The purpose of this paper is to show systematic analysis of the nonlinear susceptibilities (NS) Xn (n = 1, 2) for the exact solvable spin glass models, i.e., the Sherrington-Kirkpatrick (SK) model 71 and the spherical (SP) model of Kosteritz et al. 81 It is shown that X2 diverges proportionally to ITTsal1 in negative sign at the p.....,sc transition, but that X2 positively diverges in the F---'?P(F->SG), while X2 in the Pphase (SG-phase) is always negative. This change of sign at the transition point has not been observed in quite recent experiments by Miyako et aP1 (I) The SK model Ising spins are coupled by infinite-ranged, random interactions independently distributed with a Gaussian probability density