# Wetting transition in the McCoy-Wu model

## TL;DR

This paper investigates the wetting transition in the McCoy-Wu Ising model, revealing it is first-order and that the transition temperature varies with samples even at large lattice sizes.

## Contribution

It provides a numerical analysis showing the first-order nature of the wetting transition and the sample dependence of transition temperature in the McCoy-Wu model.

## Key findings

- Wetting transition is first-order.
- Transition temperature distribution does not narrow with larger lattices.
- Sample dependence persists in the thermodynamic limit.

## Abstract

The wetting transition is studied in the McCoy-Wu Ising model in which the random bonds are perfectly correlated in the direction parallel to the walls . The model is solved numerically on finite size lattices up to $200 \times 200^2$. It is shown that the wetting transition is first-order. For a fixed surface field, the distribution of wetting transition temperature is obtained from $1000$ samples. The results show that the deviation of the wetting transition temperature does not decreases as the lattice size increases. It is shown that for a fixed surface field the wetting transition temperature is sample dependent even in the thermodynamic limit.