Communications in Theoretical Physics

A Quantum d -Dimensional Random-Field XY Ferromagnet

Yu‐qiang Ma

Published Jun 15, 1999• 0 citations

Abstract

We propose a soluble quantum spherical XY ferromagnet with a random field in the boson space. We obtain a general expression of the critical temperature below which the ordered ferromagnet phase appears. The Imry–Ma result concerning the lower critical dimension is recovered, and the critical exponents near the critical temperature are calculated. We show that the random-field fluctuations rather than the quantum fluctuations dominate the phase transition and critical behavior of the system. The entropy vanishes as at low temperatures, contrary to the classical spherical model.

DOI: 10.1088/0253-6102/31/4/537

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Communications in Theoretical Physics

A Quantum d -Dimensional Random-Field XY Ferromagnet

Yu‐qiang Ma

Published Jun 15, 1999• 0 citations

Publisher

Abstract

DOI: 10.1088/0253-6102/31/4/537

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Effects of a random magnetic field on the phase transition of the spherical model in d space-dimensions are investigated by n->0 technique of the n-times replicated Hamiltonian.The critical temperature T, (fl.o, d) as a function of the strength fl.o of the radom field and the space dimensions d is obtained.It is shown that any critical exponent of this system is equal to that of (d-2)-dimensional pure system for sufficiently close to T,.The crossover effect from d-dimensional behavior to (d-2)-dimensional behavior is discussed.The equation of state and the universal amplitude are also obtained.Effects of a random magnetic field on the phase transition of the spherical model in d space-dimensions are investigated by n->0 technique of the n-times replicated Hamiltonian.The critical temperature T, (fl.o, d) as a function of the strength fl.o of the radom field and the space dimensions d is obtained.It is shown that any critical exponent of this system is equal to that of (d-2)-dimensional pure system for sufficiently close to T,.The crossover effect from d-dimensional behavior to (d-2)-dimensional behavior is discussed.The equation of state and the universal amplitude are also obtained.

Progress of Theoretical PhysicsOct 1, 19773 citations

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 ${\ensuremath{\mu}}_{c}.$

{\mathrm{d}}_{\mathrm{c}}

=2, where

{\mathrm{d}}_{\mathrm{c}}

is the lower critical dimension. It is shown that the critical temperature

{\mathrm{T}}_{\mathrm{c}}

below which a ferromagnetic phase appears increases with increasing the anisotropy parameter, and remains finite even for anisotropy parameter D\ensuremath{\gg}:1.

A disorder-dependent Gaussian variational approach is applied to the

d

-dimensional ferromagnetic

\mathrm{XY}

model in a random field. The randomness yields a nonextensive contribution to the variational free energy, implying a random mass term in correlation functions. The Imry-Ma low-temperature result, concerning the existence (

d>4

) or absence (

d<4

) of long-range order is obtained in a transparent way. The physical picture which emerges below

d=4

is that of a marginally stable mixture of domains. We also calculate within this variational scheme, disorder-dependent correlation functions, as well as the probability distribution of the Imry-Ma domain size.