Question

Are there classical infinite order / continuous non-symmetry breaking phase transititions besides BKT?

Answer 1

Hello user

At the Berezinskii-Kosterlitz-Thouless (BKT) phase transition, the singular part of the free energy behaves as

ξ

−2

ξ−2

, where

ξ∝

e

c/

T−

T

c

√

ξ∝ec/T−Tc

(with

c>0

c>0

) is the correlation length. Hence

ξ

ξ

has an essential singularity at

T

c

Tc

so that the free energy

f

f

is non-analytic at the phase transition. However,

f

f

is still a smooth function, thus we classify the BKT transition as an infinite order phase transition.

Furthermore, the Mermin-Wagner theorem forbids spontaneous symmetry breaking of a continuous symmetry in two dimensions at finite

T

T

. Therefore the BKT transition does not break any symmetries (and, since it is a continuous phase transition, is thus not described within Landau theory).

Answer 2

Yes there are classical infinite order.

And see in attachment