Universality in the two-dimensional dilute Baxter-Wu model

We show that accurate insights into the critical properties of the Blume–Capel model at two dimensions can be deduced from Monte Carlo simulations, even for small system sizes, when one analyses the behaviour of the zeros of the partition function. The phase diagram of the model displays a line of second-order phase transitions ending at a tricritical point, then a line of first-order transitions. We concentrate on critical and tricritical properties and compare the accuracy achieved via standard finite-size scaling of thermodynamic quantities with that from the zeros analysis. This latter analysis showcases spectacular precision, even for systems as small as 64 spins. We also show that the zeros are very sensitive to subtle crossover effects.

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Universal energy and magnetisation distributions in the Blume–Capel and Baxter–Wu models

Macêdo,

Plascak,

Vasilopoulos

et al. 2024

J. Stat. Mech.

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We analyse the probability distribution functions of the energy and magnetisation of the two-dimensional Blume–Capel (BC) and Baxter–Wu (BW) models with spin values S ∈ { 1 / 2 , 1 , 3 / 2 } in the presence of a crystal field Δ. By employing extensive single-spin flip Monte Carlo simulations and a recently developed method of studying the zeros of the energy probability distribution we are able to probe, with a good numerical accuracy, several critical characteristics of the transitions. Additionally, the universal aspects of these transitions are scrutinised by computing the corresponding probability distribution functions. The energy distribution has been underutilised in the literature when compared to that of the magnetisation. Somewhat surprisingly, however, the former appears to be more robust in characterising the universality class for both models upon varying the crystal field Δ than the latter. Finally, our analysis suggests that in contrast to the BC ferromagnet, the BW model appears to suffer from strong finite-size effects, especially upon increasing Δ and S, that obscure the application of traditional finite-size scaling approaches.

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Universality in the two-dimensional dilute Baxter-Wu model

Cited by 6 publications

References 72 publications

Critical behaviour near critical end points and tricritical points in disordered spin-1 ferromagnets

Critical behaviour near critical end points and tricritical points in disordered spin-1 ferromagnets

Critical and tricritical singularities from small-scale Monte Carlo simulations: the Blume–Capel model in two dimensions

Universal energy and magnetisation distributions in the Blume–Capel and Baxter–Wu models

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