Influence of the interaction on the heat capacity critical exponent for 1D Ising ferromagnet with periodical boundary conditions

Z.V. Dzyuba, V.N. Udodov, D.V. Spirin


The finite-dimensional scaling method was used to calculate the critical heat capacity index α. It is established that the growth of the energy parameters of the multi-spin interaction substantially affects the critical heat capacity index.In the framework of the spin flip dynamics algorithm with an original expression for the energy, an influence of the interaction of second, third neighbors, four-particle interaction, temperature and size of a 1D Ising ferromagnet on the heat capacity critical exponent is studied. Periodic border conditions are used. The critical index α is calculated by the finite size scaling method. It is established that the growth of energy parameters of the multi-spin interaction significantly affects the heat capacity exponent. Interaction energy of third neighbors decreases the value of α to a greater extent than the second-neighbor interaction J2 and four-particle one J1 – 4. Different characters of the influence of pair and four-particle interactions on α are revealed. Energy parameters are established for which this critical exponent attains negative values. For instance, taking into account the interaction energy of third neighbors, with an approach to the critical region, the heat capacity critical exponent has a minimum near negative value of α = –0.0043 ± 0.0005. With increasing number of nodes in the 1D Ising chain, heat capacity critical exponent increases. Extrapolation according to the inverse size of the system in the thermodynamic limit gives the values α = 0.19 ± 0.02, α = 0.17 ± 0.02, α = 0.20 ± 0.02, when one takes into account the interaction energy of second neighbors J2 = 0.1, third neighbors J3 = 0.1 and four-particle interaction J1 – 4 = 0.1, respectively. Note that the second neighbor and four-particle interaction energies do not change the sign of the critical exponent for N > 6, and when approaching the critical region the critical exponent α tends to zero. The results obtained are compared with the values for Ising model with "broken ends" boundary conditions, as well as with other known results for two-dimensional and three-dimensional cases.

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