The phase diagram of the gonihedric 3d Ising model via CVM

Cirillo, Emilio N. M.; Gonnella, Giuseppe; Johnston, D.A.; Pelizzola, Alessandro

doi:10.1016/s0375-9601(96)00918-8

Cited by 21 publications

(40 citation statements)

References 31 publications

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“…This fact indicates that a multicriticality with smaller emerges as j → −0.25. This observation supports the claim [19] that the nonstandard criticality reported so far [15][16][17][18][19][20] could be attributed to the end-point criticality specific to j = −0.25.…”

Section: Summary and Discussionsupporting

confidence: 90%

Multicriticality of the three-dimensional Ising model with plaquette interactions: An extension of Novotny’s transfer-matrix formalism

Nishiyama

2004

Phys. Rev. E

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A three-dimensional Ising model with the plaquette-type (next-nearest-neighbor and four-spin) interactions is investigated numerically. This extended Ising model, the so-called gonihedric model, was introduced by Savvidy and Wegner as a discretized version of the interacting (closed) surfaces without surface tension. The gonihedric model is notorious for its slow relaxation to the thermal equilibrium (glassy behavior), which deteriorates the efficiency of the Monte Carlo sampling. We employ the transfer-matrix (TM) method, implementing Novotny's idea, which enables us to treat an arbitrary number of spins N for one TM slice even in three dimensions. This arbitrariness admits systematic finite-size-scaling analyses. Accepting the extended parameter space by Cirillo et al., we analyzed the (multi-) criticality of the gonihedric model for N ഛ 13. Thereby, we found that, as first noted by Cirillo et al. analytically (cluster-variation method), the data are well described by the multicritical (crossover) scaling theory. That is, the previously reported nonstandard criticality for the gonihedric model is reconciled with a crossover exponent and the ordinary three-dimensional-Ising universality class. We estimate the crossover exponent and the correlation-length critical exponent at the multicritical point as = 0.6͑2͒ and = 0.45͑15͒, respectively.

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Section: Summary and Discussionsupporting

confidence: 90%

Multicriticality of the three-dimensional Ising model with plaquette interactions: An extension of Novotny’s transfer-matrix formalism

Nishiyama

2004

Phys. Rev. E

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“…The upper bound for β c J in 3 dimensions is consistent with values obtained from simulations [26,27] (β c J ≈ 0.505), cluster variation-Padé approximations [29] (β c J ≈ 0.550) and mean field calculations [26] (β c J ≈ 0.325).…”

Section: Introductionsupporting

confidence: 86%

“…For k > 0.3 the authors of [17,26,28,29] find a second order phase transition. It was suggested in [29], that in contrast to the case k = 0 only the ferromagnetic phases remain stable, while layered phases are thermodynamically suppressed. The low temperature expansion of the free energy in section 2 supports this picture.…”

Section: Discussionmentioning

confidence: 99%

Low temperature expansion of the gonihedric Ising model

Pietig

Wegner

1998

Nuclear Physics B

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We investigate a model of closed (d − 1)-dimensional soft-self-avoiding random surfaces on a d-dimensional cubic lattice. The energy of a surface configuration is given by E = J(n 2 + 4k n 4 ), where n 2 is the number of edges, where two plaquettes meet at a right angle and n 4 is the number of edges, where 4 plaquettes meet. This model can be represented as a Z 2 -spin system with ferromagnetic nearest-neighbour-, antiferromagnetic next-nearest-neighbour-and plaquette-interaction. It corresponds to a special case of a general class of spin systems introduced by Wegner and Savvidy. Since there is no term proportional to the surface area, the bare surface tension of the model vanishes, in contrast to the ordinary Ising model. By a suitable adaption of Peierls argument, we prove the existence of infinitely many ordered low temperature phases for the case k = 0. A low temperature expansion of the free energy in 3 dimensions up to order x 38 (x = e −βJ ) shows, that for k > 0 only the ferromagnetic low temperature phases remain stable. An analysis of low temperature expansions up to order x 44 for the magnetization, susceptibility and specific heat in 3 dimensions yields critical exponents, which are in agreement with previous results.

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“…When regarded as a model of fluctuating surfaces described by the geometric spin cluster boundaries the intention is to weight the edge length of spin clusters rather than their boundary area [32]. For κ = 0 the 3d Hamiltonians H κ display a continuous transition, possibly with 3d Ising exponents which are masked by strong crossover effects from the nearby tricritical point [33,34]. The κ = 0 plaquette Hamiltonian, on the other hand, has a strong first-order phase transition [35] and recent high-precision multicanonical simulations [36][37][38][39] have revealed that it displays non-standard finite-size scaling properties at this transition.…”

Section: Introductionmentioning

confidence: 99%

Plaquette Ising models, degeneracy and scaling

Johnston¹,

Mueller

Janke

2017

Eur. Phys. J. Spec. Top.

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Abstract. We review some recent investigations of the 3d plaquette Ising model. This displays a strong first-order phase transition with unusual scaling properties due to the size-dependent degeneracy of the low-temperature phase. In particular, the leading scaling correction is modified from the usual inverse volume behaviour ∝ 1/L 3 to 1/L 2 . The degeneracy also has implications for the magnetic order in the model which has an intermediate nature between local and global order and gives rise to novel fracton topological defects in a related quantum Hamiltonian.

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The phase diagram of the gonihedric 3d Ising model via CVM

Cited by 21 publications

References 31 publications

Multicriticality of the three-dimensional Ising model with plaquette interactions: An extension of Novotny’s transfer-matrix formalism

Multicriticality of the three-dimensional Ising model with plaquette interactions: An extension of Novotny’s transfer-matrix formalism

Low temperature expansion of the gonihedric Ising model

Plaquette Ising models, degeneracy and scaling

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