The correlation length of 3D Ising systems in the presence of an external field

Abstract

The explicit dependence of correlation length as function of temperature and external field is found for the Ising model on a simple cubic lattice near the phase transition point. , where and h _c are the renormalized values of the external field h and reduced temperature τ. The critical amplitude ξ₀ is proportional to the lattice constant through the coefficient, which is determined by the parameter of the interaction potential. The size of the critical region is established by the temperature and field. It is shown that the essential increasing of the system correlation length takes place at () with h→0 and at h′<h* (, h′=βh) with τ→0.

Keywords:

• Phase transition
• Correlation length
• External field

Notes

†Such a value of ν corresponds to the ρ⁴ model approximation at ν=0 (η is the critical exponent of the binary correlation function). Best estimates give ν= 0.630 2.