Stripe-tetragonal phase transition in the two-dimensional Ising model with dipole interactions: Partition function zeros approach

Abstract

We have performed multicanonical simulations to study the critical behavior of the two-dimensional Ising model with dipole interactions. This study concerns the thermodynamic phase transitions in the range of the interaction δ where the phase characterized by striped configurations of width h = 1 is observed. Controversial results obtained from local update algorithms have been reported for this region, including the claimed existence of a second-order phase transition line that becomes first order above a tricritical point located somewhere between δ = 0.85 and 1. Our analysis relies on the complex partition function zeros obtained with high statistics from multicanonical simulations. Finite size scaling relations for the leading partition function zeros yield critical exponents ν that are clearly consistent with a single second-order phase transition line, thus excluding such a tricritical point in that region of the phase diagram. This conclusion is further supported by analysis of the specific heat and susceptibility of the orientational order parameter.

On the Phase Diagram of the 2d Ising Model with Frustrating Dipole Interaction

“…For the model under consideration (1) it has been recently applied in Ref. [12], where the first zero of the partition function closest to the origin has been calculated for different values of interaction ratio δ at different lattice sizes L = 12 − 72. The finite size scaling (FSS) analysis of the zeros' coordinates allows one to obtain the value of the correlation length critical exponent ν.…”

“…In particular, this will allow to avoid a hyperscaling assumption while calculating the strength of the phase transition and directly obtaining the specific heat critical exponent α. The input data for our analysis are provided by the coordinates of the partition function zeros calculated in [12]. The rest of the paper is organized as follows: in sections 2 and 3 we describe the model and the method used for its analysis, our results are presented and discussed in section 4.…”

“…Subsequent MC simulations of Ref. [12] did not observe the conjectured tricritical point and resulted in the continuous phase transition for all region of δ that corresponds to the boundary between the striped h = 1 and tetragonal phases (see Fig. 1).…”

“…c P. SARKANYCH, YU. HOLOVATCH, R. KENNA, 2013 Theoretical insight into peculiarities of pattern formation in the above systems has been gained by analysing the 2d Ising model with competing ferromagnetic short-range nearest-neighbour interactions (with strength given by J) and antiferromagnetic long-range dipole interactions (of strength g) [1,[3][4][5][6][7][8][9][10][11][12]. In the framework of this model, the richness of the phase diagram is attributed to frustrations introduced by the competing character of ferromagnetic and antiferromagnetic interactions.…”

Identifying transitions in finite systems by means of partition function zeros and microcanonical inflection-point analysis: A comparison for elastic flexible polymers

“…[9][10][11]), proteins [12,13], and to polymers [14,15]. Most applications of the partition function zero analysis method are considered to be alternative approaches to scaling properties near phase transitions in large systems.…”