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Journal of the Physical Society of Japan

AlternatingS=1/2XYChain in the Lorentzian Random Field

Kiyomi Okamoto

Published Dec 15, 1990• 13 citations
Publisher

Abstract

The alternating S =1/2 XY chain in the Lorentzian random field in the z -direction is investigated by the use of the pseudo-Fermion representation. The random-averaged one-particle Green's functions for the pseudo-Fermions are exactly calculated, which enables us to exactly construct the thermodymanics of this model. The spin correlation function < S i z S j z > is also studied at T =0. The dimerized state (which is the ground state in the absence of the random field) is completely destroyed by any small (but finite) amount of the random field.

DOI
10.1143/jpsj.59.4286

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The alternating S =1/2 XY chain in the Lorentzian random field in the z -direction is investigated by the use of the pseudo-Fermion representation. The random-averaged one-particle Green's functions for the pseudo-Fermions are exactly calculated, which enables us to exactly construct the thermodymanics of this model. The spin correlation function < S i z S j z > is also studied at T =0. The dimerized state (which is the ground state in the absence of the random field) is completely destroyed by any small (but finite) amount of the random field.
We investigate the ground state of the alternating spin-1/2 XY chain with the anisotropy H = J ∑ i [1+(-1) i δ][(1+γ) S i x S i +1 x +(1-γ) S i y S i +1 y ], J >0, where 0≤γ≤1 and 0≤δ≤1. From the exact results of the ground state energy calculation, the ground state is found to be either one of the following three states: the spin fluid state (γ=δ=0), the effective singlet pair state (ES state; δ>γ) and the Néel state (γ>δ). We also exactly calculate the asymptotic form of the longitudinal spin correlation < S i z S j z > in the long distance limit. Both its functional form and the parameter dependence of the correlation length are quite consistent with our picture for the ES state and the Néel state.
We investigate the temperature dependence of the finite-field magnetization of the S = 1/2 bondalternating XY model in the Random magnetic field along the z-direction having the Lorentzian distribution.The random-averaged free energy can be exactly calculated, which enables us to obtain the thermodynamical quantities.The temperature dependence of the finite-field magnetization shows various behaviors depending on the parameters δ and Γ, where δ and Γ are the bond-alternation parameter and the Lorentzian distribution parameter, respectively.
The two-point connected correlation function, or wavevector-dependent susceptibility, of the ferromagnetic Ising chain in a random field is calculated exactly at any temperature, for a two-parameter family of diluted symmetric exponential distributions of the magnetic fields. Thermodynamic properties of this model have been derived in a previous work by the authors. Besides the correlation function itself, the solution provides exact results for the (usual) susceptibility, the correlation length and the Edwards-Anderson parameter. The low-temperature regime is examined in full detail: the authors obtain in closed form the limit value at zero temperature of various quantities, and the first correction to this limit, which behaves linearly with temperature. The correlation length is discontinuous at zero temperature. They also derive the scaling form of the correlation function for small p, where the dilution p is the probability for a spin to be subjected to a non-zero random field. Even in this limit, the correlation function is more complicated than the simple Lorentzian predicted, e.g., by mean-field theory.