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Register a new userCoulomb gas transitions in three-dimensional classical dimer models
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Close-packed, classical dimer models on three-dimensional, bipartite lattices harbor a Coulomb phase with power-law correlations at infinite temperature. Here, we discuss the nature of the thermal phase transition out of this Coulomb phase for a variety of dimer models which energetically favor crystalline dimer states with columnar ordering. For a family of these models we find a direct thermal transition from the Coulomb phase to the dimer crystal. While some systems exhibit (strong) first-order transitions in correspondence with the Landau-Ginzburg-Wilson paradigm, we also find clear numerical evidence for continuous transitions. A second family of models undergoes two consecutive thermal transitions with an intermediate paramagnetic phase separating the Coulomb phase from the dimer crystal. We can describe all of these phase transitions in one unifying framework of candidate field theories with two complex Ginzburg-Landau fields coupled to a U(1) gauge field. We derive the symmetry-mandated Ginzburg-Landau actions in these field variables for the various dimer models and discuss implications for their respective phase transitions.
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We construct models hosting classical fractal spin liquids on two realistic three-dimensional (3D) lattices of corner-sharing triangles: trillium and hyperhyperkagome (HHK). Both models involve the same form of three-spin Ising interactions on triangular plaquettes as the Newman-Moore (NM) model on the 2D triangular lattice. However, in contrast to the NM model and its 3D generalizations, their degenerate ground states and low-lying excitations cannot be described in terms of scalar cellular automata (CA), because the corresponding fractal structures lack a simplifying algebraic property, often termed the Freshmans dream. By identifying a link to matrix CAs -- that makes essential use of the crystallographic structure -- we show that both models exhibit fractal symmetries of a distinct class to the NM-type models. We devise a procedure to explicitly construct low-energy excitations consisting of finite sets of immobile defects or fractons, by flipping arbitrarily large self-similar subsets of spins, whose fractal dimensions we compute analytically. We show that these excitations are associated with energetic barriers which increase logarithmically with system size, leading to fragile glassy dynamics, whose existence we confirm via classical Monte Carlo simulations. We also discuss consequences for spontaneous fractal symmetry breaking when quantum fluctuations are introduced by a transverse magnetic field, and propose multi-spin correlation function diagnostics for such transitions. Our findings suggest that matrix CAs may provide a fruitful route to identifying fractal symmetries and fracton-like behaviour in lattice models, with possible implications for the study of fracton topological order.
The present paper considers some classical ferromagnetic lattice--gas models, consisting of particles that carry $n$--component spins ($n=2,3$) and associated with a $D$--dimensional lattice ($D=2,3$); each site can host one particle at most, thus implicitly allowing for hard--core repulsion; the pair interaction, restricted to nearest neighbors, is ferromagnetic, and site occupation is also controlled by the chemical potential $mu$. The models had previously been investigated by Mean Field and Two--Site Cluster treatments (when D=3), as well as Grand--Canonical Monte Carlo simulation in the case $mu=0$, for both D=2 and D=3; the obtained results showed the same kind of critical behaviour as the one known for their saturated lattice counterparts, corresponding to one particle per site. Here we addressed by Grand--Canonical Monte Carlo simulation the case where the chemical potential is negative and sufficiently large in magnitude; the value $mu=-D/2$ was chosen for each of the four previously investigated counterparts, together with $mu=-3D/4$ in an additional instance. We mostly found evidence of first order transitions, both for D=2 and D=3, and quantitatively characterized their behaviour. Comparisons are also made with recent experimental results.
We investigate the nature of trions, pairing and quantum phase transitions in one-dimensional strongly attractive three-component ultracold fermions in external fields. Exact results for the groundstate energy, critical fields, magnetization and phase diagrams are obtained analytically from the Bethe ansatz solutions. Driven by Zeeman splitting, the system shows exotic phases of trions, bound pairs, a normal Fermi liquid and four mixtures of these states. Particularly, a smooth phase transition from a trionic phase into a pairing phase occurs as the highest hyperfine level separates from the two lower energy levels. In contrast, there is a smooth phase transition from the trionic phase into a normal Fermi liquid as the lowest level separates from the two higher levels.
Applying Feynman diagrammatics to non-fermionic strongly correlated models with local constraints might seem generically impossible for two separate reasons: (i) the necessity to have a Gaussian (non-interacting) limit on top of which the perturbative diagrammatic expansion is generated by Wicks theorem, and (ii) the Dysons collapse argument implying that the expansion in powers of coupling constant is divergent. We show that for arbitrary classical lattice models both problems can be solved/circumvented by reformulating the high-temperature expansion (more generally, any discrete representation of the model) in terms of Grassmann integrals. Discrete variables residing on either links, plaquettes, or sites of the lattice are associated with the Grassmann variables in such a way that the partition function (and correlations) of the original system and its Grassmann-field counterpart are identical. The expansion of the latter around its Gaussian point generates Feynman diagrams. A proof-of-principle implementation is presented for the classical 2D Ising model. Our work paves the way for studying lattice gauge theories by treating bosonic and fermionic degrees of freedom on equal footing.
We consider quantum Heisenberg ferro- and antiferromagnets on the square lattice with exchange anisotropy of easy-plane or easy-axis type. The thermodynamics and the critical behaviour of the models are studied by the pure-quantum self-consistent harmonic approximation, in order to evaluate the spin and anisotropy dependence of the critical temperatures. Results for thermodynamic quantities are reported and comparison with experimental and numerical simulation data is made. The obtained results allow us to draw a general picture of the subject and, in particular, to estimate the value of the critical temperature for any model belonging to the considered class.
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