# The Tangent Space to the Manifold of Critical Classical Hamiltonians Representable by Tensor Networks

## TL;DR

This paper presents a tensor network-based Monte Carlo Renormalization Group scheme to analyze the tangent space of critical Hamiltonians in classical models, enabling precise characterization of critical points.

## Contribution

It introduces a novel tensor network approach to compute the tangent space of the manifold of critical Hamiltonians for various classical models.

## Key findings

- Computed tangent spaces for 2D and 3D Ising models
- Analyzed the 2D three-state Potts model at criticality
- Demonstrated the scheme's effectiveness in identifying critical Hamiltonians

## Abstract

We introduce a scheme to perform Monte Carlo Renormalization Group with the coupling constants of the system Hamiltonian encoded in a tensor network. With this scheme we compute the tangent space to the manifold of the critical Hamiltonians representable by a tensor network at the nearest-neighbor critical coupling for three models: the two and three dimensional Ising models and the two dimensional three-state Potts model.