Local critical behaviour at aperiodic surface extended perturbation in the Ising quantum chain

We investigate the influence of aperiodic modulations of the exchange interactions between nearest-neighbour rows on the phase transition of the two-dimensional eight-state Potts model. The systems are studied numerically through intensive Monte Carlo simulations using the Swendsen-Wang cluster algorithm for different aperiodic sequences. The transition point is located through duality relations, and the critical behaviour is investigated using FSS techniques at criticality. While the pure system exhibits a first-order transition, we show that the deterministic fluctuations resulting from the aperiodic coupling distribution are liable to modify drastically the physical properties in the neighbourhood of the transition point. For strong enough fluctuations of the sequence under consideration, a second-order phase transition is induced. The exponents β/ν, γ/ν and (1 − α)/ν are obtained at the new fixed point and crossover effects are discussed. Surface properties are also studied.

Section: Introductionmentioning

confidence: 54%

Second-order phase transition induced by deterministic fluctuations in aperiodic eight-state Potts models

Chatelain¹,

Berche

Berche³

1999

“…The scaling dimension x s e of the surface energy can be deduced from the finite-size behaviour e s = 0|σ x 1 |ε where the state |ε = η † 1 η † 2 |0 is the lowest two-particle excitated state. This matrix element can be written as [19]:…”

Section: Discussionmentioning

confidence: 99%

“…x s e = 1 + 2β s (5.12) if one assumes that φ 2 (1) scale as L −βs too. This is known to be true either for the marginal HvL model [20] or for the aperiodic version of the same model [19] where the couplings are modulated according to the Fredholm sequence [17]. When the transition is first-order, due to the localization of φ 1 , the scaling of the first excitation is anomalous [21]:…”

Section: Discussionmentioning

confidence: 99%

Aperiodic extended surface perturbations in the Ising model

Turban

1999

We study the influence of an aperiodic extended surface perturbation on the surface critical behaviour of the two-dimensional Ising model in the extreme anisotropic limit. The perturbation decays as a power κ of the distance l from the free surface with an oscillating amplitude A l = (−1) f l where f l = 0, 1 follows some aperiodic sequence with an asymptotic density equal to 1/2 so that the mean ampltitude vanishes. The relevance of the perturbation is discussed by combining scaling arguments of Cordery and Burkhardt for the Hilhorst-van Leeuwen model and Luck for aperiodic perturbations. The relevance-irrelevance criterion involves the decay exponent κ, the wandering exponent ω which governs the fluctuation of the sequence and the bulk correlation length exponent ν. Analytical results are obtained for the surface magnetization which displays a rich variety of critical behaviours in the (κ, ω)-plane. The results are checked through a numerical finite-size-scaling study. They show that second-order effects must be taken into account in the discussion of the relevance-irrelevance criterion. The scaling behaviours of the first gap and the surface energy are also discussed.

“…This is known to be true either for the marginal HvL model [20] or for the aperiodic version of the same model [19] where the couplings are modulated according to the Fredholm sequence [17]. When the transition is first-order, due to the localization of φ 1 , the scaling of the first excitation is anomalous [21]:…”

Section: Discussionmentioning

confidence: 99%

“…Furthermore we assumed that, like in Refs. [19,20], φ 2 (1) scales as L −β ′ s /2 . As for the HvL model, in the regime of first-order transition, the anomalous scaling of the first gap leads to an exponent asymmetry [5].…”

Section: Discussionmentioning

confidence: 99%

Aperiodic extended surface perturbations in the Ising model

Turban¹

1999

Abstract. We study the influence of an aperiodic extended surface perturbation on the surface critical behaviour of the two-dimensional Ising model in the extreme anisotropic limit. The perturbation decays as a power κ of the distance l from the free surface with an oscillating amplitude A l = (−1) f l where f l = 0, 1 follows some aperiodic sequence with an asymptotic density equal to 1/2 so that the mean ampltitude vanishes. The relevance of the perturbation is discussed by combining scaling arguments of Cordery and Burkhardt for the Hilhorst-van Leeuwen model and Luck for aperiodic perturbations. The relevance-irrelevance criterion involves the decay exponent κ, the wandering exponent ω which governs the fluctuation of the sequence and the bulk correlation length exponent ν. Analytical results are obtained for the surface magnetization which displays a rich variety of critical behaviours in the (κ, ω)-plane. The results are checked through a numerical finite-size-scaling study. They show that second-order effects must be taken into account in the discussion of the relevance-irrelevance criterion. The scaling behaviours of the first gap and the surface energy are also discussed.