3,552 research outputs found
Emergent Planarity in two-dimensional Ising Models with finite-range Interactions
The known Pfaffian structure of the boundary spin correlations, and more
generally order-disorder correlation functions, is given a new explanation
through simple topological considerations within the model's random current
representation. This perspective is then employed in the proof that the
Pfaffian structure of boundary correlations emerges asymptotically at
criticality in Ising models on with finite-range interactions.
The analysis is enabled by new results on the stochastic geometry of the
corresponding random currents. The proven statement establishes an aspect of
universality, seen here in the emergence of fermionic structures in two
dimensions beyond the solvable cases.Comment: 59 pages, 19 figure
Box Graphs and Singular Fibers
We determine the higher codimension fibers of elliptically fibered Calabi-Yau
fourfolds with section by studying the three-dimensional N=2 supersymmetric
gauge theory with matter which describes the low energy effective theory of
M-theory compactified on the associated Weierstrass model, a singular model of
the fourfold. Each phase of the Coulomb branch of this theory corresponds to a
particular resolution of the Weierstrass model, and we show that these have a
concise description in terms of decorated box graphs based on the
representation graph of the matter multiplets, or alternatively by a class of
convex paths on said graph. Transitions between phases have a simple
interpretation as `flopping' of the path, and in the geometry correspond to
actual flop transitions. This description of the phases enables us to enumerate
and determine the entire network between them, with various matter
representations for all reductive Lie groups. Furthermore, we observe that each
network of phases carries the structure of a (quasi-)minuscule representation
of a specific Lie algebra. Interpreted from a geometric point of view, this
analysis determines the generators of the cone of effective curves as well as
the network of flop transitions between crepant resolutions of singular
elliptic Calabi-Yau fourfolds. From the box graphs we determine all fiber types
in codimensions two and three, and we find new, non-Kodaira, fiber types for
E_6, E_7 and E_8.Comment: 107 pages, 44 figures, v2: added case of E7 monodromy-reduced fiber
Critical Loop Gases and the Worm Algorithm
The loop gas approach to lattice field theory provides an alternative,
geometrical description in terms of fluctuating loops. Statistical ensembles of
random loops can be efficiently generated by Monte Carlo simulations using the
worm update algorithm. In this paper, concepts from percolation theory and the
theory of self-avoiding random walks are used to describe estimators of
physical observables that utilize the nature of the worm algorithm. The fractal
structure of the random loops as well as their scaling properties are studied.
To support this approach, the O(1) loop model, or high-temperature series
expansion of the Ising model, is simulated on a honeycomb lattice, with its
known exact results providing valuable benchmarks.Comment: 34 pages, 12 figures; v2: 2 figures and 1 table added; v3: typo's
correcte
Non-perturbative equivalences among large N gauge theories with adjoint and bifundamental matter fields
We prove an equivalence, in the large N limit, between certain U(N) gauge
theories containing adjoint representation matter fields and their orbifold
projections. Lattice regularization is used to provide a non-perturbative
definition of these theories; our proof applies in the strong coupling, large
mass phase of the theories. Equivalence is demonstrated by constructing and
comparing the loop equations for a parent theory and its orbifold projections.
Loop equations for both expectation values of single-trace observables, and for
connected correlators of such observables, are considered; hence the
demonstrated non-perturbative equivalence applies to the large N limits of both
string tensions and particle spectra.Comment: 40 pages, JHEP styl
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