Self-consistent field near the critical point

V. Ya. Krivnov, Oleg A. Olkhov, B. N. Provotorov +1 more

P. Gluck

Paul H. E. Meijer, John C. Edwards

Applying the master equation to an Ising model, equations of motion are obtained for the average of a single spin and for the average of a pair of spins. These equations relax to equilibrium values that predict a self-consistency relationship among the internal field, temperature, and exchange energy. The critical temperature obtained is that of the Bethe approximation, and is extended to include a static external field in the magnetization direction. With this, the relaxation of an Ising model near the Curie temperature has been investigated in a self-consistent manner. The results are similar to those of Suzuki and Kubo, but in the Bethe approximation instead of the Bragg-Williams approximation, and hence predict the relaxation of the correlation as well. In particular we studied a nearly Ising spin system that is a system with relatively small isotropic transverse coupling. An oscillating, linear, and external magnetic field applied transverse to the strongly coupled direction of the spins leads to lowering of the critical temperature.

Giorgio Parisi A, Marco Picco, Nicolas Sourlas

In a previous paper (Parisi G. and Sourlas N., Phys. Rev. Lett. 89 (2002) 257204) we found that in the random field Ising model at zero temperature in three dimensions the correlation length is not self-averaging near the critical point and that the violation of self-averaging is maximal. This is due to the formation of bound states in the underlying field theory. We present a similar study for the case of disordered Potts and Ising ferromagnets in two dimensions near the critical temperature. In the random Potts model the correlation length is not self-averaging near the critical temperature but the violation of self-averaging is weaker than in the random field case. In the random Ising model we find still weaker violations of self-averaging and we cannot rule out the possibility of the restoration of self-averaging in the infinite volume limit.

E. Brézin

C. Gauvin-Ndiaye, M. Setrakian, A.–M. S. Tremblay

Near the antiferromagnetic quantum critical point (QCP) of electron-doped cuprate superconductors, angle-resolved photoemission experiments detect hot spots where the Fermi surface disappears. Here, we demonstrate, using the two-particle self-consistent theory, that in the antinodal region the Fermi liquid remains stable for a broad range of angles on the Fermi surface and for all dopings near the QCP. We show how the quasiparticle weight Z and effective mass m^{*} change and then abruptly become meaningless as the hot spots are approached. We propose a dimensionless number, easily accessible in ARPES experiments, that can be used to gauge the strength of correlations.