Finite-order correlation length for 4-dimensional weakly self-avoiding walk and $|\phi {|}^4$ spins

Abstract

We study the 4-dimensional $n$-component $|\phi {|}^4$ spin model for all integers $n\ge 1$, and the 4-dimensional continuous-time weakly self-avoiding walk which corresponds exactly to the case $n=0$ interpreted as a supersymmetric spin model. For these models, we analyse the correlation length of order $p$, and prove the existence of a logarithmic correction to mean-field scaling, with power $\frac{1}{2}\frac{n+2}{n+8}$, for all $n\ge 0$ and $p>0$. The proof is based on an improvement of a rigorous renormalisation group method developed previously.

27 pages

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Cited by in corpus (6)

• Critical exponents for long-range O(n) models below the upper critical dimension
• Self-avoiding walk, spin systems, and renormalization
• Monte Carlo study of four-dimensional self-avoiding walks of up to one billion steps
• Four-dimensional weakly self-avoiding walk with contact self-attraction
• On the existence of critical exponents for self-avoiding walks
• Non-trivial fixed point of a ${\psi }_d^4$ fermionic theory, II. Anomalous exponent and scaling operators