Abstract
In this section, we shall discuss the Suzuki-Trotter formalism, to derive the classical analogue of a quantum mechanical model and apply it to the case of pure transverse Ising model. Elliott et al [3.1] numerically established, from series studies, the equivalence of the ground state singularities of a d-dimensional transverse Ising model to those of the (d + l)-dimensional classical Ising model. Later, Suzuki [3.2], [3.3], using a generalised version of Trotter formula [3.4], analytically established that the ground state of a d-dimensional quantal spin system is equivalent to a certain (d+1)-dimensional classical Ising model with many-body interactions: the exponents associated with the ground state phase transition of the quantum system are the same as the exponents of thermal phase transition in the equivalent (d + 1)-dimensional classical model, and for d > 3 the exponents of the quantum transition assume the mean field values of the exponents of the classical model. The interaction in the classical system is finite-ranged if the original quantum system has finite-range interaction.
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(1996). Transverse Ising System in Higher Dimensions (Pure Systems). In: Quantum Ising Phases and Transitions in Transverse Ising Models. Lecture Notes in Physics Monographs, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-49865-0_3
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