Infinitely Multiple Steps in Magnetization of Ferro- and Antiferromagnetic Ising Models with Frustration on a Diamond Hierarchical Lattice

Hirose, Yuhei; Oguchi, Akihide; Fukumoto, Yoshiyuki

doi:10.7566/jpsj.83.074716

Cited by 9 publications

(5 citation statements)

References 21 publications

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“…Our solution is, simultaneously, the Migdal-Kadanoff approximation [16,17] for the cubic lattice and the exact solution [18][19][20][21][22] Exact calculations on hierarchical lattices are also currently widely used on a variety of statistical mechanics problems. [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. On the other hand, this approximation for the cubic lattice is an uncontrolled approximation, as in fact are all renormalization-group theory calculations in d = 3 and all mean-field theory calculations.…”

Section: Renormalization-group Method: Migdal-kadanoff Approximation ...mentioning

confidence: 99%

Devil's staircase continuum in the chiral clock spin glass with competing ferromagnetic-antiferromagnetic and left-right chiral interactions

Çağlar

Berker

2017

Phys. Rev. E

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The chiral clock spin-glass model with q = 5 states, with both competing ferromagnetic-antiferromagnetic and left-right chiral frustrations, is studied in d = 3 spatial dimensions by renormalization-group theory. The global phase diagram is calculated in temperature, antiferromagnetic bond concentration p, random chirality strength, and right-chirality concentration c. The system has a ferromagnetic phase, a multitude of different chiral phases, a chiral spin-glass phase, and a critical (algebraically) ordered phase. The ferromagnetic and chiral phases accumulate at the disordered phase boundary and form a spectrum of devil's staircases, where different ordered phases characteristically intercede at all scales of phase-diagram space. Shallow and deep reentrances of the disordered phase, bordered by fragments of regular and temperature-inverted devil's staircases, are seen. The extremely rich phase diagrams are presented as continuously and qualitatively changing videos.

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Section: Renormalization-group Method: Migdal-kadanoff Approximation ...mentioning

confidence: 99%

Devil's staircase continuum in the chiral clock spin glass with competing ferromagnetic-antiferromagnetic and left-right chiral interactions

Çağlar

Berker

2017

Phys. Rev. E

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“…Therefore, we restrict ourselves to the absolute zero temperature and only consider the largest term in the right hand sides of the relations given in Eqs.(3)-(5). By repeating the recursion formula several times, and choosing the largest term, we could find simple functional relations : b i = e −λ c i , a i = e −2λ c i where the value of i depends on the strength of the magnetic field and λ is function of K, B, and L [2].…”

Section: Partition Function and Recursion Relations In The N-stage Lamentioning

confidence: 99%

“…( 3)-(5). By repeating the recursion formula several times, and choosing the largest term, we could find simple functional relations : b i = e −λ c i , a i = e −2λ c i where the value of i depends on the strength of the magnetic field and λ is function of K, B, and L [2].…”

Section: Partition Function and Recursion Relations In The N-stage La...mentioning

confidence: 99%

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Exact Solutions on the Ground States of Ising Models in Magnetic Fields with Frustration on a Diamond Hierarchical Lattice

Hirose¹,

Oguchi²,

Fukumoto³

2015

Physics Procedia

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Magnetization processes of Ising models with frustration on diamond hierarchical lattices, which contain vertices with high coordination numbers, are exactly obtained at zero temperature. In antiferromagnetic systems, the magnetization cannot saturate under finite magnetic fields owing to the competition between the antiferromagnetic and Zeeman interactions and the intrinsic long-range nature of hierarchical lattices. For the zero-field classical spin-liquid phase found in [Kobayashi et al., J. Phys. Soc. Jpn. 78, 074004 (2009)], an infinitely small applied magnetic field can induce an infinitely small magnetization, despite Ising models that have discrete energy levels. By examining the structure of the partition function, we obtain the ground state spinconfigurations and clarify the mechanism of the "gapless like behavior".

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“…1 The systems consisting of diamond units with frustration have also attracted wide attention both experimentally and theoretically. [2][3][4][5][6][7][8][9][10] The diamond chain is one of the typical systems with diamond units, and it was proposed by Takano et al 2 It is a one-dimensional lattice system, and a diamond unit has two types of antiferromagnetic interactions. As shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

Ground States of Spin-1/2 Heisenberg Antiferromagnets with Frustration on a Diamond-Like-Decorated Square Lattice

2017

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We study the ground-state phase diagram of a Heisenberg model with spin S = 1 2 on a diamond-like decorated square lattice. A diamond unit has two types of antiferromagnetic exchange interactions, and the ratio λ between the length of the diagonal bond and that of the other four edges determines the strength of frustration. It has been pointed out [J. Phys. Soc. Jpn 85, 033705 (2016)] that the so-called tetramer-dimer states, which are expected to be stabilized in an intermediate region of λ c < λ < 2, are identical to the square-lattice dimer covering states, which ignited renewed interest in high-dimensional diamond-like decorated lattices. In order to determine the phase boundary λ c , we employ the modified spin wave method to estimate the energy of the ferrimagnetic state and obtain λ c = 0.974. Our obtained magnetizations for spin-1 2 sites and for spin-1 sites are m = 0.398 andm = 0.949, and spin reductions are 20 % and 5%, respectively. This indicates that spin fluctuation is much smaller than that of the S = 1 2 square-lattice antiferromagnet: thus, we can consider that our obtained ground-state energy is highly accurate. Further, our numerical diagonalization study suggests that other cluster states do not appear in the ground-state phase diagram. IntroductionThe exploration of frustration in quantum spin models has been one of the most interesting issues in condensed matter physics. 1 The systems consisting of diamond units with frustration have also attracted wide attention both experimentally and theoretically. 2-10The diamond chain is one of the typical systems with diamond units, and it was proposed by Takano et al. 2 It is a one-dimensional lattice system, and a diamond unit has two types of antiferromagnetic interactions. As shown in Fig. 1 (a), solid and dashed lines, respectively, represent exchange parameters J and J ′ , and the ratio λ = J ′ /J determines the ground-state properties. It has been known that, in the case of spin J. Phys. Soc. Jpn. DRAFT S = 1 2 , three types of ground-state phases exist: the dimer-monomer (DM) state for 2 < λ, the tetramer-dimer (TD) state for 0.909 < λ < 2, and the ferrimagnetic state for λ < 0.909. 2 In the TD state, as shown in Fig. 1 (a), diamond units with triplet pairs (shaded blue ovals) and with singlet pairs (unshaded red ovals) are arranged alternately. This arrangement results from the fact that for λ < 2, the energy decreases as the number of triplet pairs increases, but nearest-neighbor repulsion exists between two diamond units with triplet pairs, which can be explained by the variational principle and the Lieb-Mattice theorem. 2, 3 In the TD state, the edge spins, which are represented by the small open circles in Fig. 1 (a), always belong to a tetramer. Furthermore, as we will show later, the singlet pair on the dotted lines makes the four interactions J in the diamond unit vanish effectively. We note that the above-mentioned property of a tetramer is that of a dimer in the dimer covering model. If we regard a tetramer as a "dimer", we can ident...

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Infinitely Multiple Steps in Magnetization of Ferro- and Antiferromagnetic Ising Models with Frustration on a Diamond Hierarchical Lattice

Cited by 9 publications

References 21 publications

Devil's staircase continuum in the chiral clock spin glass with competing ferromagnetic-antiferromagnetic and left-right chiral interactions

Devil's staircase continuum in the chiral clock spin glass with competing ferromagnetic-antiferromagnetic and left-right chiral interactions

Exact Solutions on the Ground States of Ising Models in Magnetic Fields with Frustration on a Diamond Hierarchical Lattice

Ground States of Spin-1/2 Heisenberg Antiferromagnets with Frustration on a Diamond-Like-Decorated Square Lattice

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