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arXiv:1303.1594 · International Symposium on Nanoscience and Quantum Physics (nanoPHYS)

Randomness Effect on the Temperature Dependence of the Finite Field Magnetization of a One-Dimensional Spin Gapped System

Kiyomi Okamoto

Published Jan 14, 2015• 0 citations
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Abstract

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.

DOI
10.7566/jpscp.4.013003

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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.
We present an exact solution of a one-dimensional XY\mathrm{XY}XY model in a random magnetic field in the limit of strong-field pinning. The structure factor exhibits Lorentzian-squared behavior at nonzero temperatures. The scaling behavior of the correlation length as a function of randomness is different from that obtained in the weak-field pinning regime. We also study the dynamical behavior of the system using a simple relaxational model. The magnetization decays anomalously with time as ${t}^{\frac{7}{6}}{e}^{{\ensuremath{-}ct}^{\frac{1}{3}}}$.
The one-dimensional X-Y model in a z axis magnetic field with random coupling constants is studied. The free energy is calculated for the case in which the squares of the coupling constants have a generalized Poisson distribution. The effect of randomness in the coupling constants on the low-temperature thermodynamics is studied. In particular, it is found that a phase transition which occurs at zero temperature in the non-random system disappears in the random system. The thermodynamic quantities which are singular in the non- random system have derivatives of all orders in the random system.
Analytic results for the free energy, magnetic structure factor, and Edwards-Anderson order parameter of a one-dimensional ferromagnetic Ising model in a random magnetic field are obtained. The structure factor consists of both Lorentzian and Lorentzian-squared terms at all temperatures (TTT) greater than zero; the Lorentzian-squared terms vanish at T=0T=0T=0. The calculated correlation length agrees with predictions of the Imry-Ma domain argument.
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.