We report a numerical study of the bond-diluted two-dimensional Potts model using transfer-matrix calculations. For different numbers of states per spin, we show that the critical exponents at the random fixed point are the same as in self-dual random-bond cases. In addition, we determine the multifractal spectrum associated with the scaling dimensions of the moments of the spin-spin correlation function in the cylinder geometry. We show that the behaviour is fully compatible with the one observed in the random-bond case, confirming the general picture according to which a unique fixed point describes the critical properties of different classes of disorder: dilution, self-dual binary random bond, self-dual continuous random bond.We report a numerical study of the bond-diluted two-dimensional Potts model using transfer-matrix calculations. For different numbers of states per spin, we show that the critical exponents at the random fixed point are the same as in self-dual random-bond cases. In addition, we determine the multifractal spectrum associated with the scaling dimensions of the moments of the spin-spin correlation function in the cylinder geometry. We show that the behaviour is fully compatible with the one observed in the random-bond case, confirming the general picture according to which a unique fixed point describes the critical properties of different classes of disorder: dilution, self-dual binary random bond, self-dual continuous random bond.

arXiv:cond-mat/0108014Journal of Physics A Mathematical and GeneralNov 6, 200115 citations

Long-range quenched bond disorder in the bidimensional Potts model

Francesco Chippari, Marco Picco, Raoul Santachiara

Abstract We study the bidimensional q-Potts model with long-range bond correlated disorder. Similarly to Chatelain (2014 Phys. Rev. E 89 032105), we implement a disorder bimodal distribution by coupling the Potts model to auxiliary spin-variables, which are correlated with a power-law decaying function. The universal behaviour of different observables, especially the thermal and the order-parameter critical exponents, are computed by Monte-Carlo techniques for q = 1 , 2 , 3 -Potts models for different values of the power-law decaying exponent a. On the basis of our conclusions, which are in agreement with previous theoretical and numerical results for q = 1 and q = 2, we can conjecture the phase diagram for q ∈ [ 1 , 4 ] . In particular, we establish that the system is driven to a fixed point at finite or infinite long-range disorder depending on the values of q and a. Finally, we discuss the role of the higher cumulants of the disorder distribution. This is done by drawing the auxiliary spin-variables from different statistical models. While the main features of the phase diagram depend only on the first and second cumulant, we argue, for the infinite disorder fixed point, that certain universal effects are affected by the higher cumulants of the disorder distribution.Abstract We study the bidimensional q-Potts model with long-range bond correlated disorder. Similarly to Chatelain (2014 Phys. Rev. E 89 032105), we implement a disorder bimodal distribution by coupling the Potts model to auxiliary spin-variables, which are correlated with a power-law decaying function. The universal behaviour of different observables, especially the thermal and the order-parameter critical exponents, are computed by Monte-Carlo techniques for q = 1 , 2 , 3 -Potts models for different values of the power-law decaying exponent a. On the basis of our conclusions, which are in agreement with previous theoretical and numerical results for q = 1 and q = 2, we can conjecture the phase diagram for q ∈ [ 1 , 4 ] . In particular, we establish that the system is driven to a fixed point at finite or infinite long-range disorder depending on the values of q and a. Finally, we discuss the role of the higher cumulants of the disorder distribution. This is done by drawing the auxiliary spin-variables from different statistical models. While the main features of the phase diagram depend only on the first and second cumulant, we argue, for the infinite disorder fixed point, that certain universal effects are affected by the higher cumulants of the disorder distribution.

arXiv:2301.13727Journal of Statistical Mechanics Theory and ExperimentApr 1, 20239 citations

Boundary critical behaviour of two-dimensional random Potts \n\tmodels

Gábor Palágyi, Christophe Chatelain, Bertrand Berche +1 more

\n \nUsing extensive Monte Carlo simulations, transfer matrix techniques \nand\nconformal invariance, ferromagnetic random\n $q-$ state Potts models for $3\\le q\\le 8$ are studied in the vicinity \nof the \ncritical temperature.\nIn particular the surface and bulk magnetization exponents $\\beta_1$ \nand \nβ are found\nmonotonically increasing with q. At the critical temperature, \ndifferent \nmoments (n)\nof the magnetization profiles are calculated which are all found \nto accurately follow predictions of \nconformal invariance. The critical correlation functions \nshow multifractal behaviour, the decay exponents of the different \nmoments\nboth in the volume and at the surface, are $n-$ dependent.\n \n\n\n \nUsing extensive Monte Carlo simulations, transfer matrix techniques \nand\nconformal invariance, ferromagnetic random\n$q-$state Potts models for $3\\le q\\le 8$ are studied in the vicinity \nof the \ncritical temperature.\nIn particular the surface and bulk magnetization exponents $\\beta_1$ \nand \nβ are found\nmonotonically increasing with q. At the critical temperature, \ndifferent \nmoments (n)\nof the magnetization profiles are calculated which are all found \nto accurately follow predictions of \nconformal invariance. The critical correlation functions \nshow multifractal behaviour, the decay exponents of the different \nmoments\nboth in the volume and at the surface, are $n-$dependent.\n \n\n

Oct 19, 20124 citations

Critical correlation functions of the Potts model

Bernard Nienhuis

Physica A Statistical Mechanics and its ApplicationsMar 1, 19981 citation

\n \nUsing extensive Monte Carlo simulations, transfer matrix techniques \nand\nconformal invariance, ferromagnetic random\n

q-

state Potts models for

3\\le q\\le 8

are studied in the vicinity \nof the \ncritical temperature.\nIn particular the surface and bulk magnetization exponents

\\beta_1

\nand \nβ are found\nmonotonically increasing with q. At the critical temperature, \ndifferent \nmoments (n)\nof the magnetization profiles are calculated which are all found \nto accurately follow predictions of \nconformal invariance. The critical correlation functions \nshow multifractal behaviour, the decay exponents of the different \nmoments\nboth in the volume and at the surface, are

n-

dependent.\n \n\n