Correlation functions on the critical lines of the Baxter and Ashkin-Teller models

Kadanoff, Leo P.; Brown, Amanda

doi:10.1016/0003-4916(79)90100-3

Cited by 307 publications

(202 citation statements)

References 12 publications

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“…However, the exponents are not constant as they change with the average connectivity in the network. The variation of critical exponents along a critical line is similar to the Ashkin-Teller and 8-vertex models [49][50][51].…”

Section: Discussionsupporting

confidence: 57%

Strain-driven criticality underlies nonlinear mechanics of fibrous networks

et al. 2016

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Networks with only central force interactions are floppy when their average connectivity is below an isostatic threshold. Although such networks are mechanically unstable, they can become rigid when strained. It was recently shown that the transition from floppy to rigid states as a function of simple shear strain is continuous, with hallmark signatures of criticality [Sharma et al., Nature Phys. 12, 584 (2016)]. The nonlinear mechanical response of collagen networks was shown to be quantitatively described within the framework of such mechanical critical phenomenon. Here, we provide a more quantitative characterization of critical behavior in subisostatic networks. Using finite-size scaling we demonstrate the divergence of strain fluctuations in the network at well-defined critical strain. We show that the characteristic strain corresponding to the onset of strain stiffening is distinct from but related to this critical strain in a way that depends on critical exponents. We confirm this prediction experimentally for collagen networks. Moreover, we find that the apparent critical exponents are largely independent of the spatial dimensionality. With subisostaticity as the only required condition, strain-driven criticality is expected to be a general feature of biologically relevant fibrous networks.

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Section: Discussionsupporting

confidence: 57%

Strain-driven criticality underlies nonlinear mechanics of fibrous networks

et al. 2016

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“…The relations (14) are the extended scaling laws conjectured by Kadanoff [4] and Luther and Peschel [5]. The critical indices, as functions of λ, are non-universal and depend on all details of the model; however, such nonuniversality is all contained in the function K(λ) (which is expressed in our analysis as a convergent power series expansion), and the indices have a simple universal expressions in terms of the parameter K.…”

Section: Introduction and Main Resultsmentioning

confidence: 67%

Universality Relations in Non-solvable Quantum Spin Chains

Benfatto

Mastropietro

2010

J Stat Phys

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“…Following the analysis of den Nijs et al [4] for the antiferromagnetic threestate Potts model on a square lattice, the most important vortex excitations which drive the critical phase into the disordered phase are the bound pairs of vortex states (Figs.2(e) and 2(f )) which have vorticity of ±6 (Fig.4). The scaling dimension of these excitations can be obtained by using the well-known relation between scaling dimensions for excitations of different vorticities such as [15] …”

Section: Mapping To the Vertex Model And Stability Analysismentioning

confidence: 99%

Three-state Potts model on a triangular lattice

Park

1994

Phys. Rev. B

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We study the phase diagram of the three-state Potts model on a triangular lattice with general interactions (ferro/antiferromagnetic) between nearest neighbor spins. When the interactions along two lattice-vector directions are antiferromagnetic and infinitely strong, this model becomes equivalent to a six-vertex model and exhibits a first-order (KDP) transition from an ordered phase into a critical phase. Comparing the excitations occurred by relaxing the restriction of infinite-strength interactions and those in the eight-vertex model, we analytically obtain the critical index for those excitations and demonstrate the existence of a critical phase for the case of finite antiferromagnetic interactions in two directions and ferromagnetic interactions in the other direction. When the interactions are antiferromagnetic in all three directions, Monte Carlo simulations show that a first-order line emerges from the KDP point and separates completely an ordered phase and a disordered phase. Along the special line where all three antiferromagnetic interactions have the same strength, the cell-spin analysis reveals that the symmetry of the ground states is dual to the symmetry of the n = 3 ferromagnetic cubic model which is known to exhibit a first-order phase transition.

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Correlation functions on the critical lines of the Baxter and Ashkin-Teller models

Cited by 307 publications

References 12 publications

Strain-driven criticality underlies nonlinear mechanics of fibrous networks

Strain-driven criticality underlies nonlinear mechanics of fibrous networks

Universality Relations in Non-solvable Quantum Spin Chains

Three-state Potts model on a triangular lattice

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