Solving the 3d Ising Model with the Conformal Bootstrap II. c Minimization and Precise Critical Exponents
Abstract
We use the conformal bootstrap to perform a precision study of the operator spectrum of the critical 3d Ising model. We conjecture that the 3d Ising spectrum minimizes the central charge c in the space of unitary solutions to crossing symmetry. Because extremal solutions to crossing symmetry are uniquely determined, we are able to precisely reconstruct the first several {Z}_2 even operator dimensions and their OPE coefficients. We observe that a sharp transition in the operator spectrum occurs at the 3d Ising dimension ∆ _σ = 0.518154(15) , and find strong numerical evidence that operators decouple from the spectrum as one approaches the 3d Ising point. We compare this behavior to the analogous situation in 2d, where the disappearance of operators can be understood in terms of degenerate Virasoro representations.
 Publication:

Journal of Statistical Physics
 Pub Date:
 June 2014
 DOI:
 10.1007/s1095501410427
 arXiv:
 arXiv:1403.4545
 Bibcode:
 2014JSP...157..869E
 Keywords:

 Critical phenomena;
 Conformal invariance;
 Ising Model;
 Critical exponents;
 Central charge;
 Stress tensor;
 High Energy Physics  Theory;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Lattice;
 Mathematical Physics
 EPrint:
 55 pages, many figures