Localizing the Ising CFT from the ground state of the Ising model on the fuzzy sphere

Kay Jörg Wiese
CNRS-Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Universités, Université Paris-Diderot, Sorbonne Paris Cité 24 rue Lhomond, 75005 Paris, France

Abstract

We locate the phase-transition line for the Ising model on the fuzzy sphere from a finite-size scaling analysis of its ground-state energy. This is similar to what was used to locate the complex CFT of the 5-state Potts model in dimension $d=2$ [PRL 133 (2024) 077101]. There it was shown that a CFT is characterized by a stationarity condition for the measured effective central charge. Our strategy is to write the ground-state energy as $E_{\rm GS}(N)/N_m = E_{0} + E_1 /N_m + E_{3/2}/N_m^{3/2}+ ...$, and to search for a minimum of $ E_{3/2}/E_0$ as a function of the couplings. This procedure finds the critical curve of [PRX 13 (2023) 021009] with good precision, and their sweet spot as well. We find similar results when normalizing by the gap to the stress tensor tensor $T$ or first parity-odd operator $\sigma$.

arXiv:2510.09482 [pdf]