A revised Ising model in which all the interactions among the electrons are taken into account on the basis of the mean-field theory is proposed. By determining the partition function, that there exists the phase transition in our model is found. The magnetic transition temperature (Curie temperature) and Curie-Wiess equation of our model are also obtained.

Journal of Wenzhou Teachers CollegeJan 1, 20040 citations

Journal of Magnetism and Magnetic Materials

Two-dimensional Ising transition in one-dimensional interacting electrons

Hiromi Otsuka, Masaaki Nakamura

Published Nov 8, 2006• 0 citations

Publisher

DOI: 10.1016/j.jmmm.2006.10.306

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n{x}_{0}

, where

n

is the electron density and

{x}_{0}

is the characteristic length of the transverse confining potential. If this transition occurs in the low-density limit, it can be understood as the deformation of the one-dimensional Wigner crystal to a zigzag arrangement of the electrons described by an Ising order parameter. The critical properties are governed by the charge degrees of freedom and the spin sector remains essentially decoupled. At large densities, on the other hand, the transition is triggered by the filling of a second one-dimensional subband of transverse quantization. Electrons at the bottom of the second subband interact strongly due to the diverging density of states and become impenetrable. We argue that this stabilizes the electron liquid as it suppresses pair-tunneling processes between the subbands that would otherwise lead to an instability. However, the impenetrable electrons in the second band are screened by the excitations of the first subband, so that the transition is identified as a Lifshitz transition of impenetrable polarons. We discuss the resulting phase diagram as a function of

n{x}_{0}