Statistical Mechanics
Spontaneous symmetry breaking in 2D supersphere sigma models and applications to intersecting loop soups (1810.07807v2)
Etienne Granet, Jesper Lykke Jacobsen, Hubert Saleur
2018-10-17
Two-dimensional sigma models on superspheres
are known to flow to weak coupling
in the IR when
. Their long-distance properties are described by a free 'Goldstone' conformal field theory (CFT) with
bosonic and
fermionic degrees of freedom, where the
symmetry is spontaneously broken. This behavior is made possible by the lack of unitarity. The purpose of this paper is to study logarithmic corrections to the free theory at small but non-zero coupling
. We do this in two ways. On the one hand, we perform perturbative calculations with the sigma model action, which are of special technical interest since the perturbed theory is logarithmic. On the other hand, we study an integrable lattice discretization of the sigma models provided by vertex models and spin chains with
Adaptive Cluster Expansion for Ising spin models (1906.05805v1)
Simona Cocco, Giancarlo Croce, Francesco Zamponi
2019-06-13
We propose an algorithm to obtain numerically approximate solutions of the direct Ising problem, that is, to compute the free energy and the equilibrium observables of spin systems with arbitrary two-spin interactions. To this purpose we use the Adaptive Cluster Expansion method, originally developed to solve the inverse Ising problem, that is, to infer the interactions from the equilibrium correlations. The method consists in iteratively constructing and selecting clusters of spins, computing their contributions to the free energy and discarding clusters whose contribution is lower than a fixed threshold. The properties of the cluster expansion and its performance are studied in detail on one dimensional, two dimensional, random and fully connected graphs with homogeneous or heterogeneous fields and couplings. We discuss the differences between different representations (boolean and Ising) of the spin variables.
Transition from a Dirac spin liquid to an antiferromagnet: Monopoles in a QED3-Gross-Neveu theory (1905.02750v2)
Éric Dupuis, M. B. Paranjape, William Witczak-Krempa
2019-05-07
We study the quantum phase transition from a Dirac spin liquid to an antiferromagnet driven by condensing monopoles with spin quantum numbers. We describe the transition in field theory by tuning a fermion interaction to condense a spin-Hall mass, which in turn allows the appropriate monopole operators to proliferate and confine the fermions. We compute various critical exponents at the quantum critical point (QCP), including the scaling dimensions of monopole operators by using the state-operator correspondence of conformal field theory. We find that the degeneracy of monopoles in QED3 is lifted and yields a non-trivial monopole hierarchy at the QCP. In particular, the lowest monopole dimension is found to be smaller than that of QED3 using a large
expansion where
is the number of fermion flavors. For the minimal magnetic charge, this dimension is
at leading order. We also study the QCP between Dirac and chiral spin liquids, which allows us to test a conjectured duality to a bosonic CP
theory. Finally, we discuss the implications of our results for quantum magnets on the Kagome lattice.
Absence of superfluidity in 2D dipolar Bose striped crystals (1906.05782v1)
Fabio Cinti, Massimo Boninsegni
2019-06-13
We present results of computer simulations at low temperature of a two-dimensional system of dipolar bosons, with dipole moments aligned at an arbitrary angle with respect to the direction perpendicular to the plane. The phase diagram includes a homogeneous superfluid phase, as well as triangular and striped crystalline phases, as the particle density and the tilt angle are varied. In the striped solid, no phase coherence among stripes and consequently no ``supersolid" phase is found, in disagreement with recent theoretical predictions.
Diverse communities behave like typical random ecosystems (1904.02610v2)
Wenping Cui, Robert Marsland III, Pankaj Mehta
2019-04-01
With a brief letter to Nature in 1972, Robert May triggered a worldwide research program in theoretical ecology and complex systems that continues to this day. Building on powerful mathematical results about large random matrices, he argued that systems with sufficiently large numbers of interacting components are generically unstable. In the ecological context, May's thesis directly contradicted the longstanding ecological intuition that diversity promotes stability. In economics and finance, May's work helped to consolidate growing concerns about the fragility of an increasingly interconnected global marketplace. In this Letter, we draw on recent theoretical progress in random matrix theory and statistical physics to fundamentally extend and reinterpret May's theorem. We confirm that a wide range of ecological models become unstable at the point predicted by May, even when the models do not strictly follow his assumptions. Surprisingly, increasing the interaction strength or diversity beyond the May threshold results in a reorganization of the ecosystem -- through extinction of a fixed fraction of species -- into a new stable state whose properties are well described by purely random interactions. This self-organized state remains stable for arbitrarily large ecosystem and suggests a new interpretation of May's original conclusions: when interacting complex systems with many components become sufficiently large, they will generically undergo a transition to a "typical" self-organized, stable state.
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