EPJ B Highlight - Calculating the impact of domain walls on systems’ free energies

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Published on 17 October 2025

Mathematical approach improves calculations of how phase boundaries affect a material’s properties

The behaviours of many materials are strongly influenced by abrupt boundaries between different phases, called domain walls. In particular, the patterns in which domain walls arrange themselves are closely connected to a material’s free energy: a temperature-dependent quantity representing the balance between a system’s tendency toward low energy and high entropy.

Through new analysis published in EPJ B, a collaboration of European researchers have developed and applied a method that accounts for all possible arrangements of domain walls within a model system. By providing a robust approach for calculating its free energy, including finite-size effects, their method could help improve models of a wide array of structures where domain walls play a key role.

Applying a method originally introduced by D. B. Abraham, the authors modelled an Ising cylinder, where atomic spins are arranged in an orderly cylindrical lattice and can be either aligned or anti-aligned with their neighbours. In this system, phases are represented by differing patterns of alignment and anti-alignment between neighbouring spins – and are separated by abrupt boundaries.

Under any given set of boundary conditions, the researchers were able to account for all possible spin configurations, allowing them to closely represent the domain walls that emerge in real materials. Their approach incorporates surface tension – the energy required to sustain a domain wall, and point tension – associated with the endpoints of a domain wall. To analyse the resulting formulas, the team used a mathematical technique that highlights the key contributions of domain wall arrangements to the system’s behaviour.

Altogether, this approach provides greater detail on how different domain wall configurations contribute to free energy within finite systems, ultimately making free energy calculations more mathematically precise, and physically interpretable in terms of large-scale features such as surface and point tensions.