Self-averaging, distribution of pseudocritical temperatures, and finite size scaling in critical disordered systems

摘要: We evaluate by Monte Carlo simulations various singular thermodynamic quantities $X$ for ensembles of quenched random Ising and Ashkin-Teller models. The measurements are taken at ${T}_{c}$ we study how the distributions $P(X)$ (and, in particular, their relative squared width, ${R}_{X})$ over ensemble depend on system size $l.$ model was studied regime where bond randomness is irrelevant found weak self-averaging; ${R}_{X}\ensuremath{\sim}{l}^{\ensuremath{\alpha}/\ensuremath{\nu}}\ensuremath{\rightarrow}0,$ $\ensuremath{\alpha}l0$ $\ensuremath{\nu}$ exponents (of pure fixed point) governing transition. For site-dilute a cubic lattice, known to be governed point, find that ${R}_{X}$ tends constant, as predicted Aharony Harris. tested whether this constant universal. However, different canonical grand disorder. identify pseudocritical temperature each sample $i,$ ${T}_{c}(i,l),$ which susceptibility reaches its maximal value ${\ensuremath{\chi}}^{\mathrm{max}}.$ distribution these dependent ${T}_{c}(i,l)$ investigated; variance scales $[\ensuremath{\delta}{T}_{c}(l){]}^{2}\ensuremath{\sim}{l}^{\ensuremath{-}2/\ensuremath{\nu}}.$ Our previously proposed finite scaling ansatz disordered systems hold. did observe deviations from single function, imply functions needed. These are, however, relatively small hence obtain statistical error it may more computationally efficient measure ${\ensuremath{\chi}}^{\mathrm{max}}$ than commonly used $\ensuremath{\chi}{(T}_{c}^{\ensuremath{\infty}}).$