Consider the free scalar field φ of mass m in two Euclidean dimensions. Its propagator is:
For small m, G is a … See more

While the Mermin–Wagner theorem prevents any spontaneous symmetry breaking on a global scale, ordering transitions of Kosterlitz–Thouless–type may be allowed. This is the case for the XY model where … See more

We will present an intuitive way to understand the mechanism that prevents symmetry breaking in low dimensions, through an application to the Heisenberg model, that is a system of n-component spins Si of … See more

Much stronger results than absence of magnetization can actually be proved, and the setting can be substantially more general. In particular :
1. The Hamiltonian can be invariant under the action o… See more

Already in 1930, Felix Bloch has argued by diagonalizing the Slater determinant for fermions, that magnetism in 2D should not exist. Some easy arguments, which are summarized below, were given by Rudolf Peierls based … See more

The image shows a (quasi-) two-dimensional crystal of colloidal particles. These are micrometre-sized particles dispersed in water and sedimented on a flat interface, thus they can perform Brownian motions onl… See more

Real magnets usually do not have a continuous symmetry, since the spin-orbit coupling of the electrons imposes an anisotropy. For atomic systems like graphene, one can show that monolayers of cosmolo… See more