Interaction effects in the spectrum of the three-dimensional Ising model

Abstract

The two-point correlation functions of statistical models show in general both poles and cuts in momentum space. The former correspond to the spectrum of massive excitations of the model, while the latter originate from interaction effects, namely creation and annihilation of virtual pairs of excitations. We discuss the effect of such interactions on the long distance behavior of correlation functions in configuration space, focusing on certain time-slice operators which are commonly used to extract the spectrum. For the 3D Ising model in the scaling region of the broken-symmetry phase, a one-loop calculation shows that the interaction effects on time-slice correlations is non negligible for distances up to a few times the correlation length, and should therefore be taken into account when analysing Monte Carlo data.

Relation between bulk order-parameter correlation function and finite-size scaling

“…For lattice systems, ξ e is an anisotropic quantity. It is expected, however, that the asymptotic ratio lim t→0+ ξ e /ξ becomes isotropic and has a universal value [14,15,16,17,18], in agreement with our results.…”

“…17) or(2.18) which was derived for the ϕ 4 model in the large-n limit in Sect. 3 and in one-loop order in Sect.…”

Bound-state energy of the three-dimensional Ising model in the broken-symmetry phase: Suppressed finite-size corrections

“…On one hand, little attention has been paid to the low-lying spectrum. Recent consideration on the Ising model, however, revealed rich characters in the low-lying spectrum [1,2,3,4,5,6,7,8,9,10]. Actually, in the broken-symmetry phase, the magnetic excitations are attractive, forming a pair of bound states with characteristic excitation gap {m i }.…”

“…The detailed structure of the d = 3 spectrum is not fully understood. So far, the lowest bound state m 2 , namely, the second-excitation gap, has been studied in detail [4,5,6,7,8,9,10]; a series of bound states is considered in Refs. [4,7,8,10,11].…”

Non-perturbative states in the three-dimensional ø4 theory

“…Let us analyze in more detail what we expect from perturbative φ 4 theory in this respect: a simple one-loop computation (see Ref. [5]) shows that the cut in the momentum space propagator implies for the time slice correlators the behavior…”