Finite-Size Scaling in the p-State Mean-Field Potts Glass: A Monte Carlo Investigation |
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Authors: | O Dillmann W Janke K Binder |
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Institution: | (1) Institut für Physik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany;(2) Institut für Theoretische Physik, Universität Leipzig, D-04109 Leipzig, Germany |
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Abstract: | The p-state mean-field Potts glass with bimodal bond distribution (±J) is studied by Monte Carlo simulations, both for p = 3 and p = 6 states, for system sizes from N = 5 to N = 120 spins, considering particularly the finite-size scaling behavior at the exactly known glass transition temperature T
c. It is shown that for p = 3 the moments q
(k) of the spin-glass order parameter satisfy a simple scaling behavior,
being the appropriate scaling function and T the temperature. Also the specific heat maxima have a similar behavior,
, while moments of the magnetization scale as
. The approach of the positions T
max of these specific heat maxima to T
c as N is nonmonotonic. For p = 6 the results are compatible with a first-order transition, q
(k) (q
jump)k as N but since the order parameter q
jump at T
c is rather small, a behavior q
(k) N
-k/3
as N also is compatible with the data. Thus no firm conclusions on the finite-size behavior of the order parameter can be drawn. The specific heat maxima c
V
max
behave qualitatively in the same way as for p = 3, consistent with the prediction that there is no latent heat. A speculative phenomenological discussion of finite-size scaling for such transitions is given. For small N (N 15 for p = 3, N 12 for p = 6) the Monte Carlo data are compared to exact partition function calculations, and excellent agreement is found. We also discuss ratios
, for various quantities X, to test the possible lack of self-averaging at T
c. |
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Keywords: | Mean-field Potts glass orientational glass infinite range interactions Monte Carlo simulations finite-size scaling self-averaging first-order transition without latent heat |
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