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- W2022934484 startingPage "P02028" @default.
- W2022934484 abstract "In statistical mechanics, observables are usually related to local degrees of freedom such as the Q<4 distinct states of the Q-state Potts models or the heights of the restricted solid-on-solid models. In the continuum scaling limit, these models are described by rational conformal field theories, namely the minimal models for suitable p,p'. More generally, as in stochastic Loewner evolution (SLEκ), one can consider observables related to non-local degrees of freedom such as paths or boundaries of clusters. This leads to fractal dimensions or geometric exponents related to values of conformal dimensions not found among the finite sets of values allowed by the rational minimal models. Working in the context of a loop gas with loop fugacity β = −2cos(4π/κ), we use Monte Carlo simulations to measure the fractal dimensions of various geometric objects such as paths and the generalizations of cluster mass, cluster hull, external perimeter and red bonds. Specializing to the case where the SLE parameter κ = (4p'/p) is rational with p<p', we argue that the geometric exponents are related to conformal dimensions found in the infinitely extended Kac tables of the logarithmic minimal models . These theories describe lattice systems with non-local degrees of freedom. We present results for critical dense polymers , critical percolation , the logarithmic Ising model , the logarithmic tricritical Ising model as well as . Our results are compared with rigorous results from SLEκ, with predictions from theoretical physics and with other numerical experiments. Throughout, we emphasize the relationships between SLEκ, geometric exponents and the conformal dimensions of the underlying CFTs." @default.
- W2022934484 created "2016-06-24" @default.
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- W2022934484 date "2009-02-10" @default.
- W2022934484 modified "2023-10-02" @default.
- W2022934484 title "Geometric exponents, SLE and logarithmic minimal models" @default.
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- W2022934484 doi "https://doi.org/10.1088/1742-5468/2009/02/p02028" @default.
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