Modified effective-field approach to low-dimensional spin-1/2 systems

Abstract

Two different generalization schemes for the molecular field approximation are described. Both contain the possibility to incorporate generalized effective fields that induce correlations between the degrees of freedom at the boundary of a chosen cluster. Applications are presented for low-dimensional spin-1/2 systems. For the Ising models the critical couplings and critical exponents as well as the spontaneous magnetization curve are determined. An application of the method to the quantum Sϭ 1 2 one-dimensional Heisenberg model is presented and reliable low-temperature estimates of the specific heat are evaluated. The data are combined with the quantum transfer matrix predictions for large system sizes and this leads to the following prediction for the low-temperature specific heat: CϭAT ␣ with ␣ϭ0.35Ϯ0.07. ͓S1063-651X͑97͒08006-9͔

Effects of selective dilution on phase diagram and ground-state magnetizations of an Ising antiferromagnet on triangular and honeycomb lattices

“…However, in this work we adopt the simplest approximation which neglects correlations between different spins but it takes the single-site kinematic relations exactly into account through the Var der Waerden identity. It is worthwhile noticing that this approach gives the same values of the critical temperature for the two-and three-dimensional Ising ferromagnets as the lowest linear approximation within the modified effective-field theory [14] in the so called P scheme. Consequently, the present EFT yields, for example, a nonzero critical concentration for quenched diluted systems, the lack of order in the one-dimensional Ising ferromagnet, and the occurrence of order in the two-dimensional case with the critical temperature improved over the usual mean-field theory [13] (for another advanced effective-field methods see also, e.g., Ref.…”

Field-dependent specific heat and magnetization for the S=12 antiferromagnetic chain Yb4As3: simulation and experiments

“…We have tested our simulations for the finite chains using the results obtained from the exact diagonalization technique for the limit B ¼ 0 [8]. In Fig.…”

Application of Algebraic Combinatorics to Finite Spin Systems with Dihedral Symmetry

“…In many actual applications one deals with bipartite antiferromagnets [1], so the case of N even seems to be more important, however the other case (N odd) is discussed for three, at least, reasons: (i) the ground state energy of infinite linear antiferromagnets is approximated from below and above by those obtained in the cases of even-and odd-sized rings, respectively [4]; (ii) there are still some open problem related with linear ferromagnets (e.g. critical exponents near T = 0 K [9]); in this case the parity of N is (almost) irrelevant; (iii) the presented considerations and results are more complete. In Sec.…”