Abstract. We derive an exact expression of the response function to an infinitesimal magnetic field for an Ising-Glauber-like model with arbitrary exchange couplings. The result is expressed in terms of thermodynamic averages and does not depend on the initial conditions or on the dimension of the space. The response function is related to time-derivatives of a complicated correlation function and so the expression is a generalisation of the equilibrium fluctuation-dissipation theorem in the special case of this model. Correspondence with the Ising-Glauber model is discussed. A discretetime version of the relation is implemented in Monte Carlo simulations and then used to study the aging regime of the ferromagnetic two-dimensional Ising-Glauber model quenched from the paramagnetic phase to the ferromagnetic one. Our approach has the originality to give direct access to the response function and the fluctuation-dissipation ratio.

We study by Monte Carlo simulations the influence of bond dilution on the three-dimensional Ising model. This paradigmatic model in its pure version displays a second-order phase transition with a positive specific heat critical exponent α. According to the Harris criterion disorder should hence lead to a new fixed point characterized by new critical exponents. We have determined the phase diagram of the diluted model, between the pure model limit and the percolation threshold. For the estimation of critical exponents, we have first performed a finite-size scaling study, where we concentrated on three different dilutions. We emphasize in this work the great influence of the cross-over phenomena between the pure, disorder and percolation fixed points which lead to effective critical exponents dependent on the concentration. In a second set of simulations, the temperature behaviour of physical quantities has been studied in order to characterize the disorder fixed point more accurately. In particular this allowed us to estimate ratios of some critical amplitudes. In accord with previous observations for other models this provides stronger evidence for the existence of the disorder fixed point since the amplitude ratios are more sensitive to the universality class than the critical exponents. Moreover, the question of non-self-averaging at the disorder fixed point is investigated and compared with recent results for the bond-diluted q = 4 Potts model. Overall our numerical results provide evidence that, as expected on theoretical grounds, the critical behaviour of the bond-diluted model is governed by the same universality class as the site-diluted model.

We study by extensive Monte Carlo simulations the effect of random bond dilution on the phase transition of the three-dimensional four-state Potts model that is known to exhibit a strong first-order transition in the pure case. The phase diagram in the dilution-temperature plane is determined from the peaks of the susceptibility for sufficiently large system sizes. In the strongly disordered regime, numerical evidence for softening to a second-order transition induced by randomness is given. Here a large-scale finite-size scaling analysis, made difficult due to strong crossover effects presumably caused by the percolation fixed point, is performed.

The self-dual random-bond eight-state Potts model is studied numerically through large-scale Monte Carlo simulations using the Swendsen-Wang cluster flipping algorithm. We compute bulk and surface order parameters and susceptibilities and deduce the corresponding critical exponents at the random fixed point using standard finite-size scaling techniques. The scaling laws are suitably satisfied. We find that a belonging of the model to the 2D Ising model universality class can be conclusively ruled out, and the dimensions of the relevant bulk and surface scaling fields are found to take the values y h = 1.849, yt = 0.977, y hs = 0.54, to be compared to their Ising values: 15/8, 1, and 1/2.The understanding of the role played by impurities on the nature of phase transitions is of great importance, both from experimental and theoretical perspectives. It is a quite active field of research where the resort to large-scale Monte Carlo simulations is often necessary [1]. The effect of quenched bond randomness in a system which undergoes, in the homogeneous case, a secondorder phase transition has been extensively studied. It is well understood since Harris proposed a relevance criterion for the fluctuating interactions [2]. Disorder appears to be a relevant perturbation when the specific heat exponent α of the pure system is positive. Since in the two-dimensional Ising model (IM) α vanishes due to the logarithmic Onsager singularity, this model was carefully studied in the '80s [3].The analogous situation when the pure system exhibits a first-order transition was less well studied, in spite of the early work of Imry and Wortis who argued that quenched disorder could induce a secondorder phase transition [4]. This argument was then rigourously proved by Aizenman and Wehr, and Hui and Berker [5]. In two dimensions, even an infinitesimal amount of quenched impurities changes the transition into a second-order one. The first intensive Monte Carlo study of the effect of disorder at a first-order phase transition is due to Chen, Ferrenberg and Landau (CFL). These authors studied the q = 8-state two-dimensional Potts model, which, in the pure case, is known to exhibit a first-order phase transition when q > 4 [6]. They definitively showed that the transition becomes secondorder in the presence of bond randomness [7], and obtained the critical exponents from a finite-size scaling (FSS) study at the critical point of a self-dual disordered system [8]. Their results, together with other related works [10,11], suggested that any two-dimensional random system should belong to the 2D pure IM universality class [12]. In a recent paper, Cardy and Jacobsen (CJ) used a different approach [13], based on a transfer matrix formalism [14], to study random-bond Potts models for different values of q. Their estimation of the critical exponents leads to a continuous variation of β b /ν with q. This result is in accordance with previous theoretical calculations when q ≤ 4 [15], and, in the randomnessinduced second-order phase transition regime q...

This work is a contribution to the study of universality in out-of-equilibrium lattice models undergoing a second-order phase transition at equilibrium. The experimental protocol that we have chosen is the following: the system is prepared in its high-temperature phase and then quenched at the critical temperature Tc. We investigated by mean of Monte Carlo simulations two quantities that are believed to take universal values: the exponent λ/z obtained from the decay of autocorrelation functions and the asymptotic value X∞ of the fluctuation-dissipation ratio X(t, s). This protocol was applied to the Ising model, the 3-state clock model and the 4-state Potts model on square, triangular and honeycomb lattices and to the Ashkin-Teller model at the point belonging at equilibrium to the 3-state Potts model universality class and to a multispin Ising model and the Baxter-Wu model both belonging to the 4-state Potts model universality class at equilibrium.