Progress of Theoretical Physics

Phase Transitions in Gaussian Random Magnetic Fields

Fumihiko Tanaka

Published Oct 1, 1977• 3 citations

Abstract

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.

DOI: 10.1143/ptp.58.1166

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Progress of Theoretical Physics

Phase Transitions in Gaussian Random Magnetic Fields

Fumihiko Tanaka

Published Oct 1, 1977• 3 citations

Publisher

Abstract

DOI: 10.1143/ptp.58.1166

Related papers

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arXiv:cond-mat/9503041Physical review. B, Condensed matterSep 1, 1995138 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 ${\ensuremath{\mu}}_{c}.$

{\mathit{h}}_{\mathit{r}}

{)}^{2}

being close to one this gives further support for a two-exponent scaling scenario implying \ensuremath{\eta}\ifmmode\bar\else\textasciimacron\fi{}=2\ensuremath{\eta}. The magnetization behaves discontinuously at the transition, i.e., \ensuremath{\beta}=0. However, no divergence for the specific heat and in particular no latent heat is found. Also the probability distribution of the magnetization does not show a multipeak structure that would be characteristic for the phase-coexistence at first-order phase-transition points.