Scaling and criticality in dilute systems

Martin Hasenbusch B, Francesco Parisen Toldin, Andrea Pelissetto C +1 more

We present a finite-size scaling analysis of high-statistics Monte Carlo simulations of the three-dimensional randomly site-diluted and bond-diluted Ising model. The critical behaviour of these systems is affected by slowly decaying scaling corrections which make the accurate determination of their universal asymptotic behaviour quite hard, requiring an effective control of the scaling corrections. For this purpose we exploit improved Hamiltonians, for which the leading scaling corrections are suppressed for any thermodynamic quantity, and improved observables, for which the leading scaling corrections are suppressed for any model belonging to the same universality class. The results of the finite-size scaling analysis provide strong numerical evidence that phase transitions in three-dimensional randomly site-diluted and bond-diluted Ising models belong to the same randomly dilute Ising universality class. We obtain accurate estimates of the critical exponents, ν = 0.683(2), η = 0.036(1), α = −0.049(6), γ = 1.341(4), β = 0.354(1), δ = 4.792(6), and of the leading and next-to-leading correction-to-scaling exponents, ω = 0.33(3) and ω 2 = 0.82(8).

Robin B. Stinchcombe

Robin B. Stinchcombe

A phenomenological scaling method is used to obtain exact renormalisation-group transformations for pure and bond-diluted transverse Ising chains at zero temperature. An exact discussion is given of basic critical properties of the two systems, and the exponents characterising the quantum and percolative critical behaviour of the correlation length of the dilute chain are found to be nu lambda = nu rho =1.

Guangping Zheng, Mo Li

Critical short-time dynamics in a bond-diluted Ising model is investigated in this paper using numerical simulations. The effective static and dynamic critical exponents determined by the power-law scaling are found to depend strongly on bond concentration and initial state. For weak disorder, the short-time scaling relations for the system quenched from high temperature are observed to hold. In the strong dilution limit, multiscaling relations for the system starting from the ordered state are found. Corrections to the short-time scaling are proposed. The effect of disorder on critical short-time dynamics is discussed.

N. S. Tonchev, Angelos Angelopoulos, Takis Fildisis