simulations and exact results for small sizes

Abstract. The use of parameters measuring order-parameter fluctuations (OPF) has been encouraged by the recent results reported in referenece [2,3] which show that two of these parameters, G and Gc, take universal values in the limT!0. In this paper we present a detailed study of parameters measuring OPF for two mean-eld models with and without time-reversal symmetry which exhibit dierent patterns of replica symmetry breaking below the transition: the Sherrington-Kirkpatrick model with and without a eld and the Ising p-spin glass (p = 3). We give numerical results and analyze the consequences which replica equivalence imposes on these models in the innite volume limit. We give evidence for the transition in each system and discuss the character of nite-size eects. Furthermore, a comparative study between this new family of parameters and the usual Binder cumulant analysis shows what kind of new information can be extracted from the nite T behavior of these quantities. The two main outcomes of this work are: 1) Parameters measuring OPF give better estimates than the Binder cumulant for Tc and even for very small systems they give evidence for the transition. 2) For systems with no time-reversal symmetry, parameters de ned in terms of connected quantities are the proper ones to look at. PACS. 75.10.Nr Spin-glass and other random models { 05.50.+q Lattice theory and statistics (Ising, Potts, etc.) { 75.40.Gb Dynamic properties (dynamic susceptibility, spin waves, spin diusion, dynamic scaling, etc.) { 75.40.Mg Numerical simulation studies