[show abstract][hide abstract] ABSTRACT: We present an extensive numerical study of the critical behavior of dimer models in three dimensions, focusing on the phase transition between Coulomb and crystalline columnar phases. The case of attractive interactions between parallel dimers on a plaquette was shown to undergo a continuous phase transition with critical exponents close to those of the O(N) tricritical universality class, a situation which is not easily captured by conventional field theories. That the dimer model is exactly fine-tuned to a highly symmetric point is a non trivial statement which needs careful numerical investigation. In this paper, we perform an extensive Monte Carlo study of a generalized dimer model with plaquette and cubic interactions and determine its extended phase diagram. We find that when both interactions favor alignment of the dimers, the phase transition is first order, in almost all cases. On the opposite, when interactions compete, the transition becomes continuous, with a critical exponent \eta ~ 0.2. The existence of a tricritical point between the two regimes is confirmed by simulations on very large size systems and a flowgram method. In addition, we find a highly-degenerate crystalline phase at very low temperature in the frustrated regime which is separated from the columnar phase by a first order transition. Comment: 12 pages, 13 figures
[show abstract][hide abstract] ABSTRACT: We investigate the properties of a three-leg quantum spin tube using several
techniques such as the density matrix renormalization group method, strong
coupling approaches and the non linear sigma model. For integer spins S, the
model proves to exhibit a particularly rich phase diagram consisting of an
ensemble of 2S phase transitions. They can be accurately identified by the
behavior of a non local string order parameter associated to the breaking of a
hidden symmetry in the Hamiltonian. The nature of these transitions are further
elucidated within the different approaches. We carry a detailed DMRG analysis
in the specific cases S = 1. The numerical data confirm the existence of two
Haldane phases with broken hidden symmetry separated by a trivial singlet
state. The study of the gap and of the von Neumann entropy suggest a first
order phase transition but at the close proximity of a tricritical point
separating a gapless and a first order transition line in the phase diagram of
the quantum spin tube.
[show abstract][hide abstract] ABSTRACT: We study a phase transition in a 3D lattice gauge theory, a "coarse-grained" version of a classical dimer model. Duality arguments indicate that the dimer lattice theory should be dual to a XY model coupled to a gauge field with geometric frustration. The transition between a Coulomb phase with dipolar correlations and a long range ordered columnar phase is understood in terms of a Higgs mechanism. Monte Carlo simulations of the dual model indicate a continuous transition with exponents close but apparently different from those of the 3D XY model. The continuous nature of the transition is confirmed by a flowgram analysis.