Simple mean-field approach for frustrated antiferromagnets on hexagonal lattices, aimed to describe the high-temperature part of temperature-magnetic field phase diagram, is proposed. It shown, that an interplay between modulation vector symmetry, Zeeman energy and magneto-dipolar interaction leads stabilization triple-$Q$ skyrmion lattice in a certain region diagram. Corresponding analytical e...

Most lattice-based cryptographic schemes which enjoy a security proof suffer from huge key sizes and heavy computations. This is also true for the simpler case of identification protocols. Recent progress on ideal lattices has significantly improved the efficiency, and made it possible to implement practical lattice-based cryptography on constrained devices like FPGAs and smart phones. However,...

A simple d-dimensional lattice model is proposed, incorporating some degree of frustration and thus capable of describing some aspects of molecular orientation in covalently bound molecular solids. For d = 2 the model is shown to be equivalent to the standard two-dimensional Ising model, while for d > 2 it describes a peculiar transition from an isotropic high temperature phase to a low-dimensi...