# Exact logarithmic four-point functions in the critical two-dimensional Ising model

## TL;DR

This paper derives an exact formula for boundary four-point connectivities in the critical 2D Ising model, revealing logarithmic singularities and validated by Monte Carlo simulations, advancing understanding of Logarithmic Conformal Field Theories.

## Contribution

It provides the first exact formula for boundary four-point connectivities in the critical Ising model, highlighting logarithmic singularities and confirming predictions through simulations.

## Key findings

- Exact boundary four-point connectivity formula derived
- Logarithmic singularities identified in the solution
- Monte Carlo simulations confirm the theoretical predictions

## Abstract

Based on conformal symmetry we propose an exact formula for the four-point connectivities of FK clusters in the critical Ising model when the four points are anchored to the boundary. The explicit solution we found displays logarithmic singularities. We check our prediction using Monte Carlo simulations on a triangular lattice, showing excellent agreement. Our findings could shed further light on the formidable task of the characterization of Logarithmic Conformal Field Theories and on their relevance in physics.