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In this paper, by using Verlinde's formalism and a modified Padmanabhan'sprescription, we have obtained the lowest order quantum correction to thegravitational acceleration and MOND-type theory by considering a nonzerodifference between the number of bits of the holographic screen and number ofbits of the holographic screen that satisfy the equipartition theorem. We willalso carry out a phase transition and critical phenomena analysis in MOND-typetheory where critical exponents are obtained.

Quantum Gravitational Correction and MOND Theory in the Holographic Equipartition Scenario