Exact solution of a classical short-range spin model with a phase transition in one dimension: The Potts model with invisible states

Sarkanych, Petro; Holovatch, Yu.; Kenna, Ralph

doi:10.1016/j.physleta.2017.08.063

Cited by 18 publications

(27 citation statements)

References 35 publications

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“…For systems on scalefree networks, degree distribution exponent plays similar role. In addition, invisible states have been shown to influence the universality class with only changing entropic contribution to the free energy [15,16]. As was shown in this paper, with these two mechanisms together, the Ising model exhibits non-trivial properties.…”

Section: Discussionsupporting

confidence: 52%

“…This model was originally suggested to explain why the phase transition with the q−fold symmetry breaking undergoes a different order than predicted theoretically [7,8,9]. Analysis of this model on different lattices has been a subject of intensive analytic [10,11,12,13,14,15,16] and numerical [7,8,9] studies. It has been shown that the number of invisible states (r) plays the role of a parameter, whose increase makes the phase transition sharper.…”

Section: Introductionmentioning

confidence: 99%

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Ising model with invisible states on scale-free networks

Sarkanych

Krasnytska

2019

Physics Letters A

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We consider the Ising model with invisible states on scale-free networks. Our goal is to investigate the interplay between the entropic and topological influence on a phase transition. The former is manifest through the number of invisible states r, while the latter is controlled by the network node-degree distribution decay exponent λ. We show that the phase diagram in this case is characterised by two marginal values r c1 (λ) and r c2 (λ), which separate regions with different critical behaviours. Below the r c1 (λ) line the system undergoes only second order phase transition; above the r c2 (λ) -only a first order phase transition occurs; and in-between the lines both of these phase transitions occur at different temperatures. This behaviour differs from the one, observed on the lattice, where the Ising model with invisible states is only characterised with one marginal value r c 3.62 separating the first and second order regimes.

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Section: Discussionsupporting

confidence: 52%

Section: Introductionmentioning

confidence: 99%

Ising model with invisible states on scale-free networks

Sarkanych

Krasnytska

2019

Physics Letters A

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“…Although few one-dimensional models exhibit the phase transition [4][5][6][7], this phenomenon is related to some null elements of the transfer-matrix, which leads to a non-analytic free energy. Nevertheless, pseudo-critical temperatures have recently been investigated in onedimensional spin models [10,12].…”

Section: Discussionmentioning

confidence: 99%

“…Dauxois-Peyrard model [6], is another model with infinite transfer-matrix dimension, which can be solved numerically. More recently Sarkanych et al [7] also proposed a one-dimensional Potts model with invisible states and short-range coupling. The term invisible essentially refers to an additional energy degeneracy, which contributes to the entropy, but not the interaction energy.…”

Section: Introductionmentioning

confidence: 99%

A Conjecture on the Relationship Between Critical Residual Entropy and Finite Temperature Pseudo-transitions of One-dimensional Models

Rojas

2020

Braz J Phys

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Recently pseudo-critical temperature clues were observed in one-dimensional spin models, such as the Ising-Heisenberg spin models, among others. Here we report a relationship between the zero-temperature phase boundary residual entropy (critical residual entropy) and pseudo-transition. Usually, the residual entropy increases in the phase boundary, which means the system becomes more degenerate at the phase boundary compared with its adjacent states. However, this is not always the case; at zero temperature, there are some phase boundaries where the entropy holds the largest residual entropy of the adjacent states. Therefore, we can propose the following conjecture: If residual entropy at zero temperature is a continuous function at least from the one-sided limit at a critical point, then pseudo-transition evidence will appear at finite temperature near the critical point. We expect that this argument would apply to study more realistic models. Only by analyzing the residual entropy at zero temperature, one could identify a priori whether the system will exhibit the pseudotransition at finite temperature. To strengthen our conjecture, we use two examples of Ising-Heisenberg models, which exhibit pseudo-transition behavior: one frustrated coupled tetrahedral chain and another unfrustrated diamond chain.

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“…The second law of thermodynamics tells us that entropy increases -you can't add negative entropy. (Actually you can, but that's another story [54].) I propose the second law of impact is enlightenment via media is not negative.…”

Section: Fundamentals Of the Laws Of Impactmentioning

confidence: 95%

Two cultures: ``them and us'' in the academic world

Kenna¹

2020

Condens. Matter Phys.

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Impact of academic research onto the non-academic world is of increasing importance as authorities seek return on public investment. Impact opens new opportunities for what are known as "professional services": as scientometrical tools bestow some with confidence they can quantify quality, the impact agenda brings lay measurements to evaluation of research. This paper is partly inspired by the famous "two cultures" discussion instigated by C.P. Snow over 60 years ago. He saw a chasm between different academic disciplines and I see a chasm between academics and professional services, bound into contact through competing targets. This paper draws on my personal experience and experiences recounted to me by colleagues in different universities in the UK. It is aimed at igniting discussions amongst people interested in improving the academic world and it is intended in a spirit of collaboration and constructiveness. As a professional services colleague said, what I have to say "needs to be said". It is my pleasure to submit this paper to the Festschrift devoted to the 60th birthday of a renowned physicist, my good friend and colleague Ihor Mryglod. Ihor's role as leader of the Institute for Condensed Matter Physics in Lviv has been essential to generating some of the impact described in this paper and forms a key element of the story I wish to tell.

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Exact solution of a classical short-range spin model with a phase transition in one dimension: The Potts model with invisible states

Cited by 18 publications

References 35 publications

Ising model with invisible states on scale-free networks

Ising model with invisible states on scale-free networks

A Conjecture on the Relationship Between Critical Residual Entropy and Finite Temperature Pseudo-transitions of One-dimensional Models

Two cultures: ``them and us'' in the academic world

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