Constraint correlation functions of the one-dimensional Ising model in the scaling limit
arXiv:2509.08557 · doi:10.1103/x84b-6yhv
Abstract
We study the correlation function of the one-dimensional Ising model at fixed magnetization. Focusing on the scaling limit close to the zero-temperature fixed point, we show that this correlation function, in momentum space, exhibits surprising oscillations as a function of the magnetization. We show that these oscillations have a period inversely proportional to the momentum and give an interpretation in terms of domain walls. This is in sharp contrast with the behavior of the correlation function in constant magnetic fields, and sheds light on recent results obtained by Monte Carlo simulations for the correlation functions of the critical two-dimensional Ising model at fixed magnetization.
v1) 11 pages, 3 figures; v2) 12 pages, 5 figures, some small errors corrected
References in corpus (15)
- The nonperturbative functional renormalization group and its applications
- Probability distribution of the order parameter for the 3D Ising model universality class: a high precision Monte Carlo study
- Probability distribution of magnetization in the one-dimensional Ising model: Effects of boundary conditions
- Statistical field theory with constraints: application to critical Casimir forces in the canonical ensemble
- Finite-size effects in canonical and grand-canonical quantum Monte Carlo simulations for fermions
- Critical Binder cumulant and universality: Fortuin-Kasteleyn clusters and order-parameter fluctuations
- Nonperturbative fluctuations and metastability in a simple model: from observables to microscopic theory and back
- The effective potential, critical point scaling and the renormalization group
- Exact expressions for the partition function of the one-dimensional Ising model in the fixed- ensemble
- High-resolution Monte Carlo study of the order-parameter distribution of the three-dimensional Ising model
- Casimir versus Helmholtz forces: Exact results
- Casimir and Helmholtz forces in one-dimensional Ising model with Dirichlet (free) boundary conditions
- Generalization of the Central Limit Theorem to Critical Systems: Revisiting Perturbation Theory
- Universal and non-universal large deviations in critical systems
- Thermal transitions in a one-dimensional, finite-size Ising model