Exact and Near-Exact Inverse Renormalization Group with Constrained Monte Carlo
Abstract
We establish conditions for exactness of the inverse renormalization group via constrained Markov processes, a class of Monte Carlo simulations which sample the degrees of freedom within a block on a fine lattice under the constraint that they remain consistent with the corresponding degree of freedom on the coarse lattice according to a forward renormalization group transformation. We show analytically, for an arbitrary transformation, that constrained Markov processes correspond to an exact inversion of the renormalization group at the fixed point action, and to a near-exact inversion in the vicinity of the fixed point. We then optimize renormalization group transformations directly on inversely renormalized configurations to effectively map the action onto itself and ensure computational stability in the generation of configurations for high-dimensional systems. Starting from a set of uncorrelated configurations for the three-dimensional ϕ4 quantum field theory at lattice volume V=163, we invert the renormalization group with constrained Monte Carlo to construct a set of uncorrelated, near-equilibrium configurations for V=1283 and extract two critical exponents of the system. The inversion exhibits no critical slowing down, with dynamic critical exponent z=0.03(2).
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BibTeX
@misc{bachtis2026exact,
title = {{Exact and Near-Exact Inverse Renormalization Group with Constrained Monte Carlo}},
author = {Dimitrios Bachtis},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07641},
eprint = {2611.07641},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07641},
}
RIS
TY - UNPB
TI - Exact and Near-Exact Inverse Renormalization Group with Constrained Monte Carlo
AU - Dimitrios Bachtis
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07641
UR - https://arxiv.org/abs/2611.07641
AB - We establish conditions for exactness of the inverse renormalization group via constrained Markov processes, a class of Monte Carlo simulations which sample the degrees of freedom within a block on a fine lattice under the constraint that they remain consistent with the corresponding degree of freedom on the coarse lattice according to a forward renormalization group transformation. We show analytically, for an arbitrary transformation, that constrained Markov processes correspond to an exact inversion of the renormalization group at the fixed point action, and to a near-exact inversion in the vicinity of the fixed point. We then optimize renormalization group transformations directly on inversely renormalized configurations to effectively map the action onto itself and ensure computational stability in the generation of configurations for high-dimensional systems. Starting from a set of uncorrelated configurations for the three-dimensional ϕ^4 quantum field theory at lattice volume V=16^3, we invert the renormalization group with constrained Monte Carlo to construct a set of uncorrelated, near-equilibrium configurations for V=128^3 and extract two critical exponents of the system. The inversion exhibits no critical slowing down, with dynamic critical exponent z=0.03(2).
ER -