Fisher Exponent from Pseudo-$\epsilon$ Expansion

Abstract

Critical exponent $\eta$ for three-dimensional systems with $n$-vector order parameter is evaluated in the frame of pseudo-$\epsilon$ expansion approach. Pseudo-$\epsilon$ expansion ($\tau$-series) for $\eta$ found up to ${\tau }^7$ term for $n$ = 0, 1, 2, 3 and within ${\tau }^6$ order for general $n$ is shown to have a structure rather favorable for getting numerical estimates. Use of Padé approximants and direct summation of $\tau$-series result in iteration procedures rapidly converging to the asymptotic values that are very close to most reliable numerical estimates of $\eta$ known today. The origin of this fortune is discussed and shown to lie in general properties of the pseudo-$\epsilon$ expansion machinery interfering with some peculiarities of the renormalization group expansion of $\eta$.

arXiv comment14 pages, 4 tables, 1 figure; figure added, one number in Table IV corrected

References in corpus (23)

• Critical Phenomena and Renormalization-Group Theory
• Critical Exponents of the N-vector model
• Critical exponents and equation of state of the three-dimensional Heisenberg universality class
• Critical behavior of the three-dimensional XY universality class
• 25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice
• 3D Ising Model:The Scaling Equation of State
• Specific Heat of Liquid Helium in Zero Gravity very near the Lambda Point
• Critical exponents for 3D O(n)-symmetric model with n > 3
• The N-component Ginzburg-Landau Hamiltonian with cubic anisotropy: a six-loop study
• Precise determination of critical exponents and equation of state by field theory methods
• Exact Five-Loop Renormalization Group Functions of ${\varphi }^4$-Theory with O(N)-Symmetric and Cubic Interactions. Critical Exponents up to $\ep^5$
• Critical universality and hyperscaling revisited for Ising models of general spin using extended high-temperature series
• Five-loop renormalization-group expansions for the three-dimensional n-vector cubic model and critical exponents for impure Ising systems
• Pseudo--epsilon expansion of six--loop renormalization group functions of an anisotropic cubic model
• Fast-Convergent Resummation Algorithm and Critical Exponents of phi^4-Theory in Three Dimensions
• Extension to order ${\beta }^{23}$ of the high-temperature expansions for the spin-1/2 Ising model on the simple-cubic and the body-centered-cubic lattices
• On the criticality of frustrated spin systems with noncollinear order
• Critical behavior of two-dimensional cubic and MN models in the five-loop renormalization-group approximation
• Universal critical coupling constants for the three-dimensional n-vector model from field theory
• Harmonic crossover exponents in O(n) models with the pseudo-epsilon expansion approach
• Critical Exponents in Two Dimensions and Pseudo-ε Expansion
• Pseudo-epsilon expansion and the two-dimensional Ising model
• Pseudo-$\epsilon$ Expansion and Renormalized Coupling Constants at Criticality

Cited by in corpus (5)

• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• Critical Exponents of Superfluid Helium and Pseudo-$\epsilon$ Expansion
• Anisotropy of a Cubic Ferromagnet at Criticality
• Effective potential of the three-dimensional Ising model: the pseudo-$\epsilon$ expansion study
• Universal effective couplings of the three-dimensional $n$-vector model and field theory