Fisher exponent from pseudo-ε expansion

Area of Science:

• * Condensed Matter Physics
• * Statistical Mechanics
• * Quantum Field Theory

Background:

• * Critical exponents characterize phase transitions in physical systems.
• * The n-vector model describes systems with n-component order parameters.
• * Accurate calculation of critical exponents is crucial for understanding universality classes.

Purpose of the Study:

• * To evaluate the critical exponent eta (η) for 3D systems with an n-vector order parameter.
• * To investigate the efficacy of the pseudo-epsilon expansion approach for this calculation.
• * To compare the results with existing numerical estimates.

Main Methods:

• * Employed the pseudo-epsilon expansion (τ series) up to τ(7) for specific n values and τ(6) for general n.
• * Utilized Padé approximants and direct summation of the τ series.
• * Analyzed the convergence properties of the iteration procedures.

Main Results:

• * The pseudo-epsilon expansion for η exhibits a favorable structure for numerical estimation.
• * Iteration procedures rapidly converged to asymptotic values.
• * Obtained estimates for η closely align with the most reliable current numerical values.

Conclusions:

• * The pseudo-epsilon expansion approach provides an efficient and accurate method for calculating critical exponent η.
• * The efficiency stems from the interplay between the pseudo-epsilon expansion and renormalization group peculiarities.
• * This method offers a robust tool for theoretical physics research.