A Nontrivial Lattice Scalar Quantum Field Model
Abstract
We introduce a new Euclidean quantum model with zero-spin scaled scalar fields on a spacetime hypercubic lattice, which we refer to as the hybrid model. The model coupling parameters are the hopping parameter κ2>0 and the field interaction coupling α>0. Using the technique of lattice scaled fields, with a noncanonical scaling that corresponds to a partial renormalization (wave function renormalization), we show that the partition function of this model satisfies both thermodynamic and ultraviolet stability bounds, with constants which are uniform in the lattice volume Λs and the lattice spacing a∈(0,1]. As a consequence, the model has a finite free energy per degree of freedom in the thermodynamic limit Λsnearrow∞, at least in the subsequential sense. Subsequently, we can also take the ultraviolet or continuum limit asearrow 0. Besides the finiteness property of the free energy, for sufficiently small values of the model coupling parameters κ2 and α, we show the model satisfies Osterwalder-Schrader positivity and construct the underlying physical quantum mechanical Hilbert space, and, using a polymer expansion, we show correlations also remain bounded in the thermodynamic limit. Finally, we perturbatively compute an infinite volume truncated four-point correlation showing it is nonzero. Noting that, for fixed a, perturbation series in κ2 and α converges, these results are sufficient to show that our hybrid model makes sense as a lattice quantum field theory in spacetime dimension d=3,4, with possible extensions to other higher values of d.
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BibTeX
@misc{veiga2026nontrivial,
title = {{A Nontrivial Lattice Scalar Quantum Field Model}},
author = {P. A. Faria da Veiga and R. Mistry and M. O'Carroll},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19310},
eprint = {2610.19310},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19310},
}
RIS
TY - UNPB
TI - A Nontrivial Lattice Scalar Quantum Field Model
AU - P. A. Faria da Veiga
AU - R. Mistry
AU - M. O'Carroll
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.19310
UR - https://arxiv.org/abs/2610.19310
AB - We introduce a new Euclidean quantum model with zero-spin scaled scalar fields on a spacetime hypercubic lattice, which we refer to as the hybrid model. The model coupling parameters are the hopping parameter κ^2>0 and the field interaction coupling α>0. Using the technique of lattice scaled fields, with a noncanonical scaling that corresponds to a partial renormalization (wave function renormalization), we show that the partition function of this model satisfies both thermodynamic and ultraviolet stability bounds, with constants which are uniform in the lattice volume Λ_s and the lattice spacing a∈(0,1]. As a consequence, the model has a finite free energy per degree of freedom in the thermodynamic limit Λ_snearrow∞, at least in the subsequential sense. Subsequently, we can also take the ultraviolet or continuum limit asearrow 0. Besides the finiteness property of the free energy, for sufficiently small values of the model coupling parameters κ^2 and α, we show the model satisfies Osterwalder-Schrader positivity and construct the underlying physical quantum mechanical Hilbert space, and, using a polymer expansion, we show correlations also remain bounded in the thermodynamic limit. Finally, we perturbatively compute an infinite volume truncated four-point correlation showing it is nonzero. Noting that, for fixed a, perturbation series in κ^2 and α converges, these results are sufficient to show that our hybrid model makes sense as a lattice quantum field theory in spacetime dimension d=3,4, with possible extensions to other higher values of d.
ER -