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

Abstract

We show that the study of critical properties of the Blume-Capel model at two dimensions can be deduced from Monte Carlo simulations with good accuracy 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.

29 pages,11 figures, submitted to Journal of Statistical Mechanics: Theory and Experiment

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Cited by in corpus (13)

• Tricriticality and finite-size scaling in the triangular Blume-Capel ferromagnet
• Critical and tricritical behavior of the $d=3$ Blume-Capel model: Results from small-scale Monte Carlo simulations
• The tricritical Ising CFT and conformal bootstrap
• Transfer-matrix approach to the Blume-Capel model on the triangular lattice
• Ising's roots and the transfer-matrix eigenvalues
• On the six-loop scaling dimensions of the $({\varphi }^2{)}^n$ operators in $d=3$
• Phase transition properties via partition function zeros: The Blume-Capel ferromagnet revisited
• A Microcanonical Inflection Point Analysis via Parametric Curves and its Relation to the Zeros of the Partition Function
• Universal and non-universal signatures in the scaling functions of critical variables
• Short-time dynamics in phase-ordering kinetics
• Padé Approximation and Partition Function Zeros
• Change in the Order of a Phase Transition in the 2D Potts Model with Equivalent Neighbours
• Information-Geometric Signatures from Nonextensivity in the $1$-D Blume-Capel Model