Magnetic Equations of State in the Critical Region

Mykhailo P. Kozlovskii, Ihor V. Pylyuk, O. O. Prytula

Cyril Domb

The form of the spin pair correlation function in the critical region is investigated assuming that there is a single coherence parameter κ(t, H )( t = T / T c −1). It is found that the equation satisfied is H 2 = κ 2Δ/ν g ( t κ −1/ν ) which is closely analogous to the equation of state for magnetization H = M δ h ( tM −1/β ). The relationship between the functions g ( u ) and h ( u ) is established.

W. F. Hall, Roger E. De Wames, T. Wolfram

Michele Caselle, Martin Hasenbusch B, Andrea Pelissetto C +1 more

We compute the 2 n -point coupling constants in the high-temperature phase of the two-dimensional Ising model by using transfer-matrix techniques. This provides the first few terms of the expansion of the effective potential (Helmholtz free energy) and of the equation of state in terms of the renormalized magnetization. By means of a suitable parametric representation, we determine an analytic extension of these expansions, providing the equation of state in the whole critical region in the t , h plane.

Hazime Mori, Hisao Okamoto