Critical exponents in two dimensions and pseudo-ε expansion

Area of Science:

• * Theoretical physics
• * Statistical mechanics
• * Quantum field theory

Background:

• * Investigating critical phenomena in 2D n-vector lambda-phi-4 field models.
• * Utilizing the pseudo-epsilon expansion approach for analysis.

Purpose of the Study:

• * Derive pseudo-epsilon expansions for Wilson fixed-point location and critical exponents.
• * Obtain numerical estimates for exactly solvable models (n=1, 0, -1).

Main Methods:

• * Employing five-loop renormalization-group series.
• * Applying Padé and Padé-Borel resummation procedures.
• * Performing direct summation of pseudo-epsilon expansions.

Main Results:

• * Pseudo-epsilon expansions exhibit small lower-order coefficients and slow-growing higher-order terms.
• * Direct summation with optimal cutoff yields numerical estimates comparable to resummation methods.
• * The pseudo-epsilon expansion technique demonstrates effectiveness as a resummation method.

Conclusions:

• * The pseudo-epsilon expansion is a viable and effective technique for studying critical behavior.
• * Direct summation offers a competitive alternative to complex resummation procedures.
• * This approach simplifies the analysis of critical exponents and fixed-point locations.