TY - JOUR
T1 - Finite-Order Correlation Length for Four-Dimensional Weakly Self-Avoiding Walk and | φ| 4 Spins
AU - Bauerschmidt, Roland
AU - Slade, Gordon
AU - Tomberg, Alexandre
AU - Wallace, Benjamin C.
N1 - Publisher Copyright:
© 2016, Springer International Publishing.
PY - 2017/2/1
Y1 - 2017/2/1
N2 - We study the four-dimensional n-component | φ| 4 spin model for all integers n≥ 1 and the four-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 12n+2n+8, for all n≥ 0 and p> 0. The proof is based on an improvement of a rigorous renormalisation group method developed previously.
AB - We study the four-dimensional n-component | φ| 4 spin model for all integers n≥ 1 and the four-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 12n+2n+8, for all n≥ 0 and p> 0. The proof is based on an improvement of a rigorous renormalisation group method developed previously.
UR - http://www.scopus.com/inward/record.url?scp=84974814394&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84974814394&partnerID=8YFLogxK
U2 - 10.1007/s00023-016-0499-0
DO - 10.1007/s00023-016-0499-0
M3 - Article
AN - SCOPUS:84974814394
SN - 1424-0637
VL - 18
SP - 375
EP - 402
JO - Annales Henri Poincare
JF - Annales Henri Poincare
IS - 2
ER -