Infrared bound and mean-field behaviour in the quantum Ising model

Abstract

We prove an infrared bound for the transverse field Ising model. This bound is stronger than the previously known infrared bound for the model, and allows us to investigate mean-field behaviour. As an application we show that the critical exponent $\gamma$ for the susceptibility attains its mean-field value $\gamma =1$ in dimension at least 4 (positive temperature), respectively 3 (ground state), with logarithmic corrections in the boundary cases.

42 pages, 5 figures, to appear in CMP

References in corpus (1)

• The phase transition of the quantum Ising model is sharp

Cited by in corpus (4)

• The free energy in a class of quantum spin systems and interchange processes
• Vanishing critical magnetization in the quantum Ising model
• Decay of transverse correlations in quantum Heisenberg models
• Fermionic observables in the transverse Ising chain