Critical Behaviour of 3D Systems in the External Field

Abstract

The method for calculation of the partition function of the lattice model for the magnet in the external field near critical point is proposed. The recurrence relations and their explicit solution near the critical point are found. The critical exponents for the correlation length are obtained.

Keywords:

• Ising-like system
• critical point
• external field
• collective variables
• critical exponents

ACS number(s):

• 05.50.+q
• 64.60.Fr
• 75.10.Hk

Notes

¹In the fixed point the last equation of (8) gives (sf ₀₁)^{− 1} = 1 + α₄ h ₂*, where h ₂* = (r* + q)(u*)^{− 1/2}. Since f ₀₁ < 1 there is always the value s* such as h ₂ (s*) = 0, s* = f ₀₁ ^{− 1}. While s is close to s*, the quantity h ₂* is small. For the following calculation we use s* = 3.3783.