# Mixed Order Phase Transitions

## TL;DR

This paper reviews mixed order phase transitions, highlighting their unique features that combine aspects of first and second order transitions, using the one-dimensional Ising model with long-range interactions as a key example.

## Contribution

It provides a comprehensive review of mixed order transitions, focusing on the Ising model with long-range coupling and its relation to DNA denaturation models.

## Key findings

- Demonstrates the occurrence of mixed order transitions in the long-range Ising model
- Establishes the connection between the Ising model and the Poland-Scheraga model of DNA denaturation
- Highlights the characteristics that distinguish mixed order transitions from traditional phase transitions

## Abstract

Mixed order phase transitions are transitions which have common features with both first order and second order transitions. I review some results obtained in the context of one of the prototypical models of mixed order transitions, the one-dimensional Ising model with long-range coupling that decays as truncated inverse square distance between spins. The correspondence between this model and the Poland Scheraga model of DNA denaturation, a subject to which Michael Fisher made substantial contribution, is then outlined.