## Department of Physics Papers

#### Document Type

Journal Article

#### Date of this Version

3-1-1996

#### Publication Source

Physical Review B

#### Volume

53

#### Issue

10

#### Start Page

6362

#### Last Page

6384

#### DOI

10.1103/PhysRevB.53.6362

#### Abstract

We study the critical properties of the random field Ising model in general dimension *d* using high-temperature expansions for the susceptibility, χ=∑_{j}[〈σ_{i}σ_{j}⟩_{T}-〈σ_{i}⟩_{T}〈σ_{j}⟩_{T}]_{h} and the structure factor, *G*=∑_{j}[〈σ_{i}σ_{j}⟩_{T}]_{h}, where 〈⟩_{T} indicates a canonical average at temperature *T* for an arbitrary configuration of random fields and [ ]_{h} indicates an average over random fields. We treated two distributions of random fields, the bimodal in which each h_{i}=±h_{0} and a Gaussian distribution in which each hi has variance h_{0}^{2}. We obtained series for χ and *G* in the form ∑_{n=1,15}a_{n}(*g*,*d*)(*J*/*T*)^{n}, where *J* is the exchange constant and the coefficients a_{n}(*g*,*d*) are polynomials in *g*≡h_{0}^{2}/J^{2} and in *d*. We assume that as *T* approaches its critical value, *T*_{c}, one has χ~(*T*-*T*_{c})^{−γ} and *G*~(*T*-*T _{c}*)

^{−γ}. For dimensions above

*d*=2 we find a range of values of

*g*for which the critical exponents obtained from our series seem not to depend on

*g*. For large values of

*g*our results show a

*g*dependence which is attributable to either a tricritical point or a first-order transition. All our results for critical exponents suggest that γ

^{¯}=2γ, in agreement with the two-exponent scaling picture. In addition we have also constructed series for the amplitude ratio,

*A=(G/χ*. We find that

^{2})(T^{2})/(gJ^{2})*A*approaches a constant value as

*T*→

*T*

_{c}(consistent with γ

^{¯}=2γ) with

*A~*1. It appears that

*A*is somewhat larger for the bimodal than for the Gaussian model, in agreement with a recent analysis at high

*d*.

#### Recommended Citation

Gofman, M.,
Adler, J.,
Aharony, A.,
Harris, A.,
&
Schwartz, M.
(1996).
Critical Behavior of the Random-Field Ising Model.
*Physical Review B,*
*53*
(10),
6362-6384.
http://dx.doi.org/10.1103/PhysRevB.53.6362

**Date Posted:** 12 August 2015

This document has been peer reviewed.

## Comments

At the time of publication, author A. Brooks Harris was also affiliated with Tel Aviv University, Tel Aviv, Israel. Currently, he is a faculty member in the Physics Department at the University of Pennsylvania.