We study the quantum phase transition in the one-dimensional Ising model at zero temperature. As the strength g of the transverse field is changed, the system undergoes a quantum phase transition from an ordered to a disordered phase, characterized by spontaneous magnetization in the z-direction. We apply the standard technique of finite-size scaling in statistical mechanics to detect the nature of the quantum phase transition in the system. PACS numbers: 05.50.+q, 64.60.Cn, 64.60.Fr Keywords: Finite-size scaling, Quantum phase transition, Ising modelWe study the quantum phase transition in the one-dimensional Ising model at zero temperature. As the strength g of the transverse field is changed, the system undergoes a quantum phase transition from an ordered to a disordered phase, characterized by spontaneous magnetization in the z-direction. We apply the standard technique of finite-size scaling in statistical mechanics to detect the nature of the quantum phase transition in the system. PACS numbers: 05.50.+q, 64.60.Cn, 64.60.Fr Keywords: Finite-size scaling, Quantum phase transition, Ising model

Journal of the Korean Physical SocietyJan 15, 200715 citations

Phase transition of the two-dimensional Ising model

Tomoyasu Tanaka

Cambridge University Press eBooksMar 14, 20020 citations

On bimodal size distribution of spin clusters in the one dimensional Ising model

O. Ivanytskyi, V. Chelnokov

The size distribution of geometrical spin clusters is exactly found for the one dimensional Ising model of finite extent. For the values of lattice constant $β$ above some "critical value" $β_c$ the found size distribution demonstrates the non-monotonic behavior with the peak corresponding to the size of largest available cluster. In other words, at high values of lattice constant there are two ways to fill the lattice: either to form a single largest cluster or to create many clusters of small sizes. This feature closely resembles the well-know bimodal size distribution of clusters which is usually interpreted as a robust signal of the first order liquid-gas phase transition in finite systems. It is remarkable that the bimodal size distribution of spin clusters appears in the one dimensional Ising model of finite size, i.e. in the model which in thermodynamic limit has no phase transition at all.The size distribution of geometrical spin clusters is exactly found for the one dimensional Ising model of finite extent. For the values of lattice constant $β$ above some "critical value" $β_c$ the found size distribution demonstrates the non-monotonic behavior with the peak corresponding to the size of largest available cluster. In other words, at high values of lattice constant there are two ways to fill the lattice: either to form a single largest cluster or to create many clusters of small sizes. This feature closely resembles the well-know bimodal size distribution of clusters which is usually interpreted as a robust signal of the first order liquid-gas phase transition in finite systems. It is remarkable that the bimodal size distribution of spin clusters appears in the one dimensional Ising model of finite size, i.e. in the model which in thermodynamic limit has no phase transition at all.

arXiv:1512.02676Dec 5, 20151 citation

Phase transitions in the Ising model

Valeriy A Ryabov

Institute of Physics eBooksAug 1, 20180 citations

PHASE TRANSITIONS IN THE ISING MODEL

H Ulman, M Athematics J Ournal

Jan 1, 20100 citations

The size distribution of geometrical spin clusters is exactly found for the one dimensional Ising model of finite extent. For the values of lattice constant

β

above some "critical value"

β_c

the found size distribution demonstrates the non-monotonic behavior with the peak corresponding to the size of largest available cluster. In other words, at high values of lattice constant there are two ways to fill the lattice: either to form a single largest cluster or to create many clusters of small sizes. This feature closely resembles the well-know bimodal size distribution of clusters which is usually interpreted as a robust signal of the first order liquid-gas phase transition in finite systems. It is remarkable that the bimodal size distribution of spin clusters appears in the one dimensional Ising model of finite size, i.e. in the model which in thermodynamic limit has no phase transition at all.