We study the magnetic field effects on the diluted spin-ice materials using the replica-exchange Monte Carlo simulation. We observe five plateaus in the magnetization curve of the diluted nearestneighbor spin-ice model on the pyrochlore lattice when a magnetic field is applied in the [111] direction. This is in contrast to the case of the pure model with two plateaus. The origin of five plateaus is investigated from the spin configuration of two corner-sharing tetrahedra in the case of the diluted model. [7][8][9][10][11].In spin-ice materials, magnetic ions (Dy 3+ or Ho 3+ ) occupy the pyrochlore lattice of corner-sharing tetrahedra, and the local crystal field environment causes magnetic moments to point along the lines connecting the centers of the two tetrahedra at low temperatures. In the low-temperature spin-ice state, magnetic moments are highly constrained locally and obey the so-called "ice rules": two spins point in and two spins point out of each tetrahedron of the pyrochlore lattice. This 2-in 2-out spin configuration is equivalent to the situation for hydrogen atoms in water ice [12].The dilution effect on frustration was studied by Ke et al.[13] for spin-ice materials. Magnetic ions Dy or Ho are replaced by nonmagnetic Y ions. Nonmonotonic zeropoint entropy as a function of the dilute concentration was observed experimentally, and further studies on the dilution effects have been reported [14][15][16].In this communication, we study the diluted nearestneighbor (NN) antiferromagnetic (AFM) Ising model on the pyrochlore lattice under a magnetic field in the [111] direction. We treat the NN interaction as a theoretical model; a more complicated model, such as the dipolar model, may be required to make connections to actual materials. For the simulation method, we use the replicaexchange Monte Carlo method [17] to avoid the trap at * Electronic address: peretiatko.aa@dvfu.ru † Electronic address: nefedev.kv@dvfu.ru ‡ Electronic address: okabe@phys.se.tmu.ac.jp local-minimum configurations.We are concerned with the Hamiltonian, which is given in Eq. (2.2) of Ref. [6]; For convenience, the illustration of the pyrochlore lattice, which is a three-dimensional network of cornersharing tetrahedra, is given in Fig. 1, where the apical spins, d κ(i) = d 0 , are shown in red, whereas other spins are in blue.In the case of the site dilution of spins, the Hamiltonian becomes

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The thermodynamic properties of dipolar spin ice on square, honeycomb and shakti lattices in the long-range and shortrange dipole interaction models are studied. Exact solutions for the density of states, temperature dependencies of heat capacity, and entropy are obtained for these lattices with a finite number of point dipoles by means of complete enumeration. The magnetic susceptibility and average size of the largest low-energy cluster are calculated for square spin ice by means of Wang-Landau and Metropolis methods. We show that the long-range interaction leads to a blurring of the energy spectrum for all considered lattices. The inclusion of the long-range interaction leads to a significant change in the thermodynamic behaviour. An additional peak of heat capacity appears in the case of the honeycomb lattice. The critical temperature shifts in the direction of low or high temperatures; the direction depends on the lattice geometry. The critical temperature of the phase transition of square spin ice in the long-range model with frustrated ground states is obtained with the Wang-Landau and Metropolis methods independently.