ISSN:
1572-9613
Keywords:
Mean-field Potts glass
;
orientational glass
;
infinite range interactions
;
Monte Carlo simulations
;
finite-size scaling
;
self-averaging
;
first-order transition without latent heat
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
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, $$q^{(k)} \alpha N^{--k/3} \tilde f_k \{ N^{1/3} (1--T/T_c )\} ,{\text{ }}k = 1,2,3,...,\tilde f_k $$ being the appropriate scaling function and T the temperature. Also the specific heat maxima have a similar behavior, $$c_V^{\max } \alpha {\text{ }}const--N^{--1/3} $$ , while moments of the magnetization scale as $$m^{(k)} \alpha N^{--k/2} $$ . 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 $$R_x \equiv [(\langle X\rangle _T - [\langle X\rangle _T ]_{{\text{av}}} )^2 ]_{{\text{av}}} /[\langle X\rangle _T ]_{{\text{av}}}^2 $$ , for various quantities X, to test the possible lack of self-averaging at T c.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1023043602398
Permalink
