Correlation functions in the two-dimensional random-field Ising model

Abstract

Transfer-matrix methods are used to study the probability distributions of spin-spin correlation functions $G$ in the two-dimensional random-field Ising model, on long strips of width $L=3-15$ sites, for binary field distributions at generic distance $R$, temperature $T$ and field intensity $h_0$. For moderately high $T$, and $h_0$ of the order of magnitude used in most experiments, the distributions are singly-peaked, though rather asymmetric. For low temperatures the single-peaked shape deteriorates, crossing over towards a double-$\delta$ ground-state structure. A connection is obtained between the probability distribution for correlation functions and the underlying distribution of accumulated field fluctuations. Analytical expressions are in good agreement with numerical results for $R/L\gtrsim 1$, low $T$, $h_0$ not too small, and near G=1. From a finite-size {\it ansatz} at $T=T_c(h_0=0)$, $h_0\to 0$, averaged correlation functions are predicted to scale with $L^y{h}_0$, $y=7/8$. From numerical data we estimate y=0.875 \pm 0.025$,inexcellentagreementwiththeory.Inthesameregion,theRMSrelativewidth$W$oftheprobabilitydistributionsvariesforfixed$R/L=1$as$W \sim h_0^κ f(L h_0^u)$with$κ\simeq 0.45$,$u \simeq 0.8$;$f(x)$appearstosaturatewhen$x \to \infty$,thusimplying$W \sim h_0^κ$in$d=2$.

RevTeX code for 8 pages, 7 eps figures, to appear in Physical Review E (1999)

References in corpus (1)

• Numerical signs for a transition in the 2d Random Field Ising Model at T=0

Cited by in corpus (3)

• Strong disorder RG approach of random systems
• Susceptibility and Percolation in 2D Random Field Ising Magnets
• Correlation functions, free energies and magnetizations in the two-dimensional random-field Ising model