Scaling and renormalization group in replica-symmetry-breaking space: evidence for a simple analytical solution of the Sherrington-Kirkpatrick model at zero temperature.
Scaling and renormalization group in replica-symmetry-breaking space: evidence for a simple analytical solution of the Sherrington-Kirkpatrick model at zero temperature.
复制标题
复制对称破缺空间中的缩放和重正化群：零温度谢林顿-柯克帕特里克模型简单解析解的证据。
DOI：
10.1103/physrevlett.95.197203
复制
发表时间：
2005
影响因子：
8.6
通讯作者：
D. Sherrington
中科院分区：
文献类型：
--
作者：
R. Oppermann;D. Sherrington
利用有限复制对称破缺（RSB）序列的数值自洽解和Wilson重整化群，但RSB步数起着抽取尺度的作用，我们证明了Sherrington-Kirkpatrick自旋玻璃的Parisi序函数q（x）的非平凡T->0极限.在RSB空间的尺度支持下，不动点序函数在0<或=a<或=无穷大时被证明为q*（a）=sqrt[pi]/2 a/xi erf（xi/a），其中x/T --> a在T =0时，xi约为1.13+/-0.01。Xi在a-空间中起着相关长度的作用。q*（a）可以看作是有效一维场论的解。
Using numerical self-consistent solutions of a sequence of finite replica symmetry breakings (RSB) and Wilson's renormalization group but with the number of RSB steps playing a role of decimation scales, we report evidence for a nontrivial T-->0 limit of the Parisi order function q(x) for the Sherrington-Kirkpatrick spin glass. Supported by scaling in RSB space, the fixed point order function is conjectured to be q*(a)=sqrt[pi]/2 a/xi erf(xi/a) on 0<or=a<or=infinity, where x/T --> a at T =0 and xi approximately 1.13+/-0.01. Xi plays the role of a correlation length in a-space. q*(a) may be viewed as the solution of an effective 1D field theory.