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Universality from disorder in the random-bond Blume-Capel model

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Zierenberg,  Johannes
Department of Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Fytas, N. G., Zierenberg, J., Theodorakis, P. E., Weigel, M., Janke, W., & Malakis, A. (2018). Universality from disorder in the random-bond Blume-Capel model. Physical Review E, 97(4): 040102. doi:10.1103/PhysRevE.97.040102.


Cite as: http://hdl.handle.net/21.11116/0000-0001-3A51-3
Abstract
Using high-precision Monte Carlo simulations and finite-size scaling we study the effect of quenched disorder in the exchange couplings on the Blume-Capel model on the square lattice. The first-order transition for large crystal-field coupling is softened to become continuous, with a divergent correlation length. An analysis of the scaling of the correlation length as well as the susceptibility and specific heat reveals that it belongs to the universality class of the Ising model with additional logarithmic corrections which is also observed for the Ising model itself if coupled to weak disorder. While the leading scaling behavior of the disordered system is therefore identical between the second-order and first-order segments of the phase diagram of the pure model, the finite-size scaling in the ex-first-order regime is affected by strong transient effects with a crossover length scale L* approximate to 32 for the chosen parameters.