Rodolfo Subert | Searcharxiv

arXiv2025

From Knots to Crystals: Machine-Learned Potentials for Self-Assembling Topological Solitons in Liquid Crystals

Knotted fields in classical and quantum systems have long been recognized for their non-trivial topologies and particle-like behavior, but practical applications have been limited by the difficulty of stabilizing them. Recently, stable knotted solitonic textures--heliknotons--were discovered in chiral liquid crystals, forming adaptive crystal assemblies via elastic distortion-mediated interactions. We use machine learning to develop single-site coarse-grained potentials that accurately capture these chiral anisotropic effective interactions. The resulting potentials accurately reproduce experimentally observed heliknoton assemblies and enable simulations at length and time scales far beyond the range of fine-grained continuum models. This general framework is readily transferable to other topological solitons, providing a powerful route to understand, predict, and ultimately control their collective behavior and dynamics.

cond-mat.soft↗

arXiv2021

Geometry of the order-disorder surface of the mean-field square lattice Ising model with up to third-neighbor interactions

We revisit the field-free Ising model on a square lattice with up to third-neighbour (nnnn) interactions, also known as the $J_{1}$--$J_{2}$--$J_{3}$ model, in the mean-field approximation. Using a systematic enumeration procedure, we show that the region of phase space in which the high-temperature disordered phase is stable against all modes representing periodic magnetisation patterns up to a given size is a convex polytope that can be obtained by solving a standard vertex enumeration problem. Each face of this polytope corresponds to a set of coupling constants for which a single set of modes, equivalent up to a symmetry of the lattice, bifurcates from the disordered solution. While the structure of this polytope is simple in the halfspace $J_{3}>0$, where the nnnn-interaction is ferromagnetic, it becomes increasingly complex in the halfspace $J_{3}<0$, where the antiferromagnetic nnnn-interaction induces strong frustration. We characterize a few salient properties of these `disorder polytopes' in terms of the geometry of the space of contributing modes. We then consider the limit $N\rightarrow\infty$ giving a closed form description of the order-disorder surface in the thermodynamic limit, which shows that for $J_3 <0$ the emergent ordered phases will have a `devil's surface'-like mode structure. Finally, using Monte Carlo simulations, we show that for small periodic systems the mean-field analysis correctly predicts the dominant modes of the ordered phases that develop for coupling constants associated with the centroid of the faces of the disorder polytope.

cond-mat.stat-mech↗