Communications in Theoretical Physics

Path Integral Approach of Quantum Heisenberg Planar Spin Glass Model in the Presencesof Random Field

Yu‐qiang Ma

Published Jul 30, 1998• 0 citations

Abstract

A quantum version of the site-random Heisenberg planar XY model in a random field is presented in the boson representation. Like classical spherical model in the spin space, the model can be solved exactly within the coherent state path integral-representation. The phase diagram is obtained, and the effects of the randomness and quantum fluctuations on the onset of a spin glass phase are discussed.

DOI: 10.1088/0253-6102/30/1/121

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Communications in Theoretical Physics

Path Integral Approach of Quantum Heisenberg Planar Spin Glass Model in the Presencesof Random Field

Yu‐qiang Ma

Published Jul 30, 1998• 0 citations

Publisher

Abstract

DOI: 10.1088/0253-6102/30/1/121

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T=0

Ground-state properties of the two-dimensional

S=1/2

random Heisenberg models are investigated by the exact-diagonalization method. The phase diagram of the bond-random model (the

\pm J

model) is the same as that of the corresponding Ising spin glass model, in spite of quantum fluctuation. In the site-random model, the spin glass phase exists at least in the ferro-rich case. In comparison with the corresponding Ising model, the Néel phase of this model becomes much narrower in the ferro-rich case, while it is comparable in the antiferro-rich case. KEYWORDS: quantum spin glass, Heisenberg model, ground-state phase transition, site-random model, exact diagonalization

The quantum version of the random-field spherical

\mathrm{XY}

model on a

d

-dimensional hypercubic lattice is presented in the boson space, and solved exactly. We recover the Imry-Ma result concerning the lower critical dimension

{d}_{c}=4,

and calculate the critical exponents near the critical temperature. In particular, we obtain a general phase diagram of the model with arbitrary dimension

d

when

d>{d}_{c}.

The ferromagnetic ordering is reduced by quantum fluctuations, and destroyed completely by random-field fluctuations with sufficiently large values of the random-field variance \ensuremath{\sigma}. The entropy and the specific heat vanish as

{T}^{d/2}

at low temperatures. Since the model is equivalent to a Bose system, we show a superfluid-Mott insulator transition at a critical chemical potential ${\ensuremath{\mu}}_{c}.$