Finite-Size Effects on Symmetry Restoration in a Rotating Scalar System with Spatially Dependent Thermal Self-Energy
Abstract
We investigate ℤ2 symmetry restoration in a real λϕ4 theory confined to a finite cylindrical region undergoing rigid rotation. The finite transverse extent is imposed through Dirichlet boundary conditions, resulting in a discrete Fourier-Bessel spectrum and an explicit radial dependence of the fluctuation propagator. Using the background-field method, we derive the one-loop effective potential while retaining the spatial structure induced by the finite geometry. At finite temperature, rotation modifies the thermal mode energies through angular-momentum-dependent shifts, and the coincident-point propagator generates a position-dependent thermal self-energy that is incorporated through ring resummation. We use the resulting spatially resolved effective potential to determine the symmetry-restoration temperature Tc(Ω,R) and examine its dependence on the angular velocity and transverse size. The results show that the finite transverse size of the system modifies the symmetry-restoration temperature, leading to a nontrivial dependence of Tc(Ω,R) on R. An additional scaling behavior emerges when the normalized critical temperature is expressed in terms of the boundary velocity ΩR: systems with different transverse sizes exhibit the same relative modification of Tc when their boundary velocities are equal. This scaling persists after the inclusion of the position-dependent thermal self-energy through ring resummation, indicating that the ΩR dependence of the rotational response is maintained in the interacting finite system.
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BibTeX
@misc{castanoyepes2026finitesize,
title = {{Finite-Size Effects on Symmetry Restoration in a Rotating Scalar System with Spatially Dependent Thermal Self-Energy}},
author = {Jorge David Castaño-Yepes and Larry A. Cerón-Suárez},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34038},
eprint = {2609.34038},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34038},
}
RIS
TY - UNPB
TI - Finite-Size Effects on Symmetry Restoration in a Rotating Scalar System with Spatially Dependent Thermal Self-Energy
AU - Jorge David Castaño-Yepes
AU - Larry A. Cerón-Suárez
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.34038
UR - https://arxiv.org/abs/2609.34038
AB - We investigate ℤ_2 symmetry restoration in a real λϕ^4 theory confined to a finite cylindrical region undergoing rigid rotation. The finite transverse extent is imposed through Dirichlet boundary conditions, resulting in a discrete Fourier-Bessel spectrum and an explicit radial dependence of the fluctuation propagator. Using the background-field method, we derive the one-loop effective potential while retaining the spatial structure induced by the finite geometry. At finite temperature, rotation modifies the thermal mode energies through angular-momentum-dependent shifts, and the coincident-point propagator generates a position-dependent thermal self-energy that is incorporated through ring resummation. We use the resulting spatially resolved effective potential to determine the symmetry-restoration temperature T_c(Ω,R) and examine its dependence on the angular velocity and transverse size. The results show that the finite transverse size of the system modifies the symmetry-restoration temperature, leading to a nontrivial dependence of T_c(Ω,R) on R. An additional scaling behavior emerges when the normalized critical temperature is expressed in terms of the boundary velocity ΩR: systems with different transverse sizes exhibit the same relative modification of T_c when their boundary velocities are equal. This scaling persists after the inclusion of the position-dependent thermal self-energy through ring resummation, indicating that the ΩR dependence of the rotational response is maintained in the interacting finite system.
ER -