Estimates of critical quantities from an expansion in mass: Ising model on the simple cubic lattice

Abstract

In the Ising model on the simple cubic lattice, we describe the inverse temperature $\beta$ and other quantities relevant for the computation of critical quantities in terms of a dimensionless squared mass $M$. The critical behaviors of those quantities are represented by the linear differential equations with constant coefficients which are related to critical exponents. We estimate the critical temperature and exponents via an expansion in the inverse powers of the mass under the use of $\delta$-expansion. The critical inverse temperature ${\beta }_c$ is estimated first in unbiased manner and then critical exponents are also estimated in biased and unbiased self-contained way including $\omega$, the correction-to-scaling exponent, $\nu$, $\eta$ and $\gamma$.

19pages, many figures, based on the unpublished previous works of the author (arXiv:1303.3714 [hep-lat] and arXiv:1408.4584 [hep-lat]) with comprehensive revision. Revised version to appear in Brazilian Journal of Physics

References in corpus (10)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• A Finite Size Scaling Study of Lattice Models in the three-dimensional Ising Universality Class
• Ising exponents from the functional renormalisation group
• High-accuracy scaling exponents in the local potential approximation
• Estimate of the Critical Exponents from the Field-Theoretical Renormalization Group: Mathematical Sense of the "Standard Values"
• Delta Expansion on the Lattice and Dilated Scaling Region
• Universal Amplitude Ratios in the Ising Model in Three Dimensions
• Continuum scaling in expansions effective at a large lattice spacing
• Pade-Borel approximation of the continuum limit of strong coupling lattice fields: Two dimensional non-linear O(N) sigma model at N>=3
• Large-order aspects of the delta-expansion in low-dimensional Ising models