An Exact Result for the Partition Function of Two-Dimensional Nearest Neighbour Ising Models in Non-Zero Magnetic Field
G. Nandhini, M. V. Sangaranarayanan
本文用矩阵法导出了非零磁场中二维最近邻伊辛模型的配分函数。
The partition function of two-dimensional nearest neighbour Ising models in a non-zero magnetic field is derived employing a matrix formulation.
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Employing the exact solution of Onsager for two-dimensional Ising models, simple expressions are proposed for computing the partition function, magnetization, specific heat and susceptibility for non-zero magnetic fields of square lattices. The partition function in zero fields is also estimated and excellent agreement with the values arising from the exact solution of Onsager is demonstrated.
Partition Function for Two-Dimensional Nearest Neighbour Ising Model in a Non-Zero Magnetic Field for a Square Lattice of 16 Sites
通过系统列举十六个格点的正方形晶格的所有自旋组态，推导出有磁场存在时二维最近邻伊辛模型的配分函数的显式表达式。临界温度被证明是在良好的协议与报道的值，而相应的无量纲磁场为0.004。
Using a combinatorial method, the partition functions for two-dimensional nearest neighbour Ising models have been derived for a square lattice of 16 sites in the presence of the magnetic field. A novel hierarchical method of enumeration of all the configurations for any arrangement of sites has been proposed. This enumeration has been executed by a systematic analysis of the appropriate diagrams without employing any algorithmic approach or computational tools. The resulting algebraic eqn in terms of the magnetic field and nearest neighbour interaction energies may then provide a methodology …
The dual model for an Ising model with nearest and next-nearest neighbors
我们构造并分析了矩形格子上最近邻和次最近邻的伊辛模型的对偶模型（NNNI模型）。对偶模型的哈密顿量包含两个和四个自旋相互作用。自由费米子近似表明，四自旋相互作用引起的对偶模型的临界温度的增加被限制在有限的范围内。
Test of Universality in Anisotropic 3D Ising Model
Chen和Dohm在2004年从理论上预测，在具有多于六个最近邻的简单立方晶格上的伊辛模型中，普遍认为的普适性原理被违反。Schulte和Drope通过蒙特卡罗模拟发现了这种违反，但不是在预测的方向上。塞尔克和舒尔测试了正方形格子。在这里，我们只检查临界点附近的磁化率比的普遍性。为此目的，我们首先研究标准伊辛模型上的一个简单的立方晶格与6个最近的邻居，然后与6个最近的邻居和12次最近的邻居，并比较结果与Chen-Dohm晶格的6个最近的邻居和只有一半的12次最近的邻居。我们不确认违反普遍性发现舒尔特和Drope的易感性比率。
We consider the zero temperature coarsening in the Ising model in two dimensions where the spins interact within the Moore neighbourhood. The Hamiltonian is given by $H = - \sum_{<i,j>}{S_iS_j} - κ\sum_{<i,j'>}{S_iS_{j'}}$ where the two terms are for the first neighbours and second neighbours respectively and $κ\geq 0$. The freezing phenomena, already noted in two dimensions for $κ=0$, is seen to be present for any $κ$. However, the frozen states show more complicated structure as $κ$ is increased; e.g. local anti-ferromagnetic motifs can exist for $κ>2$. Finite sized systems also show the exi…
Microcanonical entropy of the spherical model with nearest-neighbour interactions
对于最近邻相互作用的球形模型，微正则熵s（e，m）是在热力学极限下对每个自旋的能量e和磁化强度m的所有可访问值进行解析计算的。熵函数被发现是凹的（尽管不是严格凹的），这意味着微正则和正则系综是等价的，尽管自旋必须服从球形约束的长程性质。两个过渡线被确定在（e，m）-平面，从铁磁和反铁磁分离顺磁相。将所得的微正则相图与更熟悉的正则相图进行比较。
We study phase transitions and thermodynamic properties in the two-dimensional antiferromagnetic Ising model with next-nearest-neighbor interaction on a Kagome lattice by Monte Carlo simulations. A histogram data analysis shows that a second order transition occurs in the model. From the analysis of obtained data, we can assume that next-nearest-neighbor ferromagnetic interactions in two-dimensional antiferromagnetic Ising model on a Kagome lattice excite the occurrence of a second order transition and unusual behavior of thermodynamic properties on the temperature dependence.
3D Ising Nonuniversality: a Monte Carlo study
本文利用MonteCarlo Metropolis算法研究了简单立方晶格上无外场的次近邻伊辛模型作为Ising普适类的一员。粘结剂累积量和磁化率比，这应该是普遍的量在临界点，被证明是不同的小负次近邻相互作用。
We use Monte Carlo simulation to determine the stable structures in the second-neighbour Ising model on the face-centred cubic lattice. Those structures are L1_1 for strongly antiferromagnetic second neighbour interactions and L1_0 for ferromagnetic and weakly antiferromagnetic second neighbours. We find a third stable "intermediate" antiferromagnetic phase with I4_1/amd symmetry, and calculate the paramagnetic transition temperature for each. The transition temperature depends strongly on second neighbour interactions which are not frustrated. Our results contradict a recent paper, which also…
Modulation of Local Magnetization in two-dimensional Axial-Next-Nearest-Neighbor Ising model
利用密度矩阵重整化群研究了有限温度下二维轴向次近邻伊辛模型。该模型表现出低温下的反相和高温下的调制相之间的二级相变。通过对畴壁自由能的观察，我们证实了自由费米子图像对高温侧调制周期的解释。
Phase diagram of the 3D Axial-Next-Nearest-Neighbor Ising model
用改进的张量积变分方法研究了三维轴向次近邻伊辛（ANNNI）模型。一个全球相图构建了许多公度和非公度的磁性结构。模型的魔鬼楼梯行为得到确认。自旋调制相的波长在与铁磁相的边界处增加到无穷大。的相称相的宽度是相当窄的平均场近似计算的。
The Two Dimensional XY Spin Glass with Ferromagnetic Next-Nearest-Neighbour Interactions
本文用蒙特卡罗模拟研究了正方晶格上具有铁磁次近邻相互作用的无规键XY自旋玻璃。我们发现强有力的证据，有限温度自旋玻璃转变在$T_c\approx 1.1$。我们也给出了不同的最近邻相互作用强度值的自旋玻璃临界指数的估计。我们的研究结果与普遍的行为是一致的。
Adsorption of a binary mixture of monomers with nearest-neighbour cooperative effects
考虑了具有近邻协同效应的二元混合物在一维无限晶格上的吸附模型。这两种物质的颗粒都是单体，但它们在试图吸附时所经历的排斥相互作用不同。导出了格的覆盖率的精确表达式。在干扰极限中，它是两个物种的尝试频率之间的比率的单调函数，在对应于两个单一物种中的每一个的值之间变化。这是在不同尺寸的颗粒的吸附在其他模型中获得的结果相比。研究了干扰状态的结构。
We consider the dynamics of particles undergoing the reaction $A+A \to \emptyset$ in one dimension with a dynamic bias. Here the particles move towards their nearest neighbour with probability $0.5+ε$ where $-0.5 \leq ε< 0$. $ε_c = -0.5$ is the deterministic limit where the nearest neighbour interaction is strictly repulsive. We show that the negative bias changes drastically the behaviour of the fraction of surviving particles $ρ(t)$ and persistence probability $P(t)$ with time $t$. $ρ(t)$ decays as $a/ (\log t)^b$ where $b$ increases with $ε- ε_c$. $P(t)$ shows a stretched exponential decay …
Exact solution of a two-dimensional (2D) Ising model with the next nearest interactions
本文通过修改三维伊辛模型的方法，推导了零磁场下具有次近邻相互作用的二维伊辛模型的精确解，得到了配分函数和自发磁化强度，并揭示了相互作用数或拓扑贡献的增加会提高伊辛晶格的临界点。
We find an exact general solution to the three-dimensional (3D) Ising model via an exact self-consistency equation for nearest-neighbors' correlations. It is derived by means of an exact solution to the recurrence equations for partial contractions of creation and annihilation operators for constrained spin bosons in a Holstein-Primakoff representation. In particular, we calculate analytically the total irreducible self-energy, the order parameter, the correlation functions, and the joined occupation probabilities of spin bosons. The developed regular microscopic quantum-field-theory method ha…
Despite their simple formulation, short range classical antiferromagnetic Ising models on frustrated lattices give rise to exotic phases of matter, in particular due to their macroscopic ground state degeneracy. Recent experiments on artificial spin systems comprising arrays of chirally coupled nanomagnets provide a significant strengthening of the nearest neighbour couplings compared to systems with dipolar-coupled nanomagnets. This opens the way to design artificial spin systems emulating Ising models with nearest neighbour couplings. In this paper, we compare the results of an extensive inv…
Critical Binder cumulant in two-dimensional anisotropic Ising models
本文主要用Monte Carlo方法计算了正方晶格上具有不同铁磁最近邻和次最近邻耦合的伊辛模型相变时的Binder累积量。我们讨论的可能性有关的各向同性，最近的邻居和各向异性的情况下，通过在矩形几何形状的尺度变换的临界累积量的值，以查明普遍和非普遍的功能。
We report on the development of two dual worm constructions that lead to cluster algorithms for efficient and ergodic Monte Carlo simulations of frustrated Ising models with arbitrary two-spin interactions that extend up to third-neighbours on the triangular lattice. One of these algorithms generalizes readily to other frustrated systems, such as Ising antiferromagnets on the Kagome lattice with further neighbour couplings. We characterize the performance of both these algorithms in a challenging regime with power-law correlations at finite wavevector.
Magnetization Jump in the Spin-1/2 XXZ Chain with Next-Nearest-Neighbour Coupling
研究了具有次近邻耦合α和各向异性δ的一维S=1/2自旋系统的零温磁化过程。在参数空间中存在一个区域，在该区域中，磁化强度在一定的外场下发生突变。确定了该区域的边界。这两种情况根据α <1/4或α>1/4来区分。在后一种情况下，低激发的能量色散表现出双极小结构。
Expansion of the conditional probability function in a network with nearest-neighbour degree correlations
网络的一个有用的性质，可以用来表征许多系统是度分布。然而，许多复杂的网络表现出更高阶的程度的相关性，必须通过其他手段，如聚类系数，纽曼r因子，和平均最近邻度（ANND）的研究。在本文中，我们开发了一个扩展的条件概率，可用于参数化这种程度的相关性。与该扩展相关联的度相关性的度量可以用于表示非线性相关性的存在。
Dynamical quantum phase transitions in the axial next-nearest-neighbour Ising chain
我们研究了具有扰动不可积次近邻相互作用的横场伊辛链中临界点处的突然猝灭。返回（Loschirst）振幅和相关的速率函数的表达式推导出线性顺序的下一个最近邻耦合。在热力学极限下，这些量在一组临界时刻表现出非解析行为，这种现象称为动态量子相变。我们量化的可积性破坏扰动的位置和形状，这些非解析的影响。我们的研究结果与早期的数值研究结果一致，并提供进一步的支持的断言，该模型所表现出的动态量子相变是一个通用的功能，其后淬火动力学和鲁棒性方面的列入不可积扰动。
Next nearest neighbour Ising models on random graphs
本文发展了随机图上次近邻伊辛模型的结果。除了作为一个重要的组成部分，在经典模型的挫折系统，第二邻居相互作用的相互作用自然出现在几个应用程序，如颜色多样性问题和图形游戏。我们展示了随机图，包括定期连接图，有一个周期性变化的自由能，与最近的下一个最近的耦合的比率，或最近的邻居的平均数的合奏。当耦合比为整数时，在零温下可以观察到顺磁相。这被示出为与相互作用的锁定或解锁性质有关。对于反铁磁耦合，自旋玻璃相在低温下被证明。交互结构被公式化为一个因素图，在树上的解决方案开发。利用腔体方法推导了复型对称性能量一步复本对称性破缺解。我们计算在这些框架内的相图，并证明存在的动态转变在零温度下的情况下，反铁磁耦合的规则和非均匀的随机图。
Planar lattice gases with nearest-neighbour exclusion
讨论了蜂窝格上的硬六边形和硬正方形问题以及相应的问题。当活动是统一的情况下是组合学家感兴趣的，是没有两个相邻的1的二进制矩阵计数的问题。对于这种情况下，我们使用强大的角转移矩阵方法来数值计算每个站点的配分函数，密度和一些近邻的相关性，以高精度。特别是对于正方形格子，我们得到的配分函数每个网站的43位小数。
A series of symmetry-protected topological(SPT) and trivial spin-gap phases in the spin-1/2 ferromagnetic--antiferromagnetic alternating Heisenberg chain with alternating next-nearest-neighbour interaction are investigated using two kinds of entanglement spectra defined by different divisions of the whole chain. In the case one of the next-nearest-neighbor interaction vanishes, the model reduces to the $Δ$-chain in which a series of spin-gap phases are found in J. Phys. Soc. Jpn. 77, 044707 (2008). From the degeneracy of the entanglement spectra, these phases are identified as the SPT and triv…
It is known that the normal three-dimensional (3D) Ising model on a cubic lattice is dual to the Wegner's 3D $Z_2$ lattice gauge theory. Here we find an unusual $Z_2$ lattice gauge theory which is dual to the 3D Ising model with not only nearest-neighbor (nn) coupling, but also next-nearest-neighbor (nnn) coupling. Our gauge theory has on each edge four $Z_2$ variables that have product $+1$, each located on a vector perpendicular to the edge. The nn coupling in the Ising model maps to the plaquette term in the gauge theory where the four variables multiplied have their vectors pointing inward…
Phase diagram and critical behavior of the square-lattice Ising model with competing nearest- and next-nearest-neighbor interactions
采用并行回火算法和GPU加速技术，在均匀磁场作用下，对具有相同强度的反铁磁（排斥）最近邻（NN）和次最近邻（NNN）相互作用的正方晶格上的伊辛模型进行了大规模蒙特卡罗模拟.从（2x1）和行移位（2x2）有序相到顺磁相的转变都是连续的。从我们的数据分析，（2 × 1）的临界线和双临界点，分离的两个有序相在T=0的再入行为被证实。根据我们沿相边界得到的临界指数，铃木的弱普适性似乎成立。
New critical behaviour of the three-dimensional Ising model with nearest-neighbor, next-nearest-neighbor and plaquette interactions
本文用集团变分方法的立方体和星立方体近似以及最近提出的集团变分-Padé近似方法研究了具有最近邻、次最近邻和元胞相互作用的简单立方伊辛模型的临界和多临界行为。特别注意的是铁磁-顺磁相变的临界终点线：其（多）临界指数的计算，其值表明，过渡属于一个新的普适类。交叉指数的粗略估计也给出了。
Topological Phases of the Spin-1/2 Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chain with Frustrated Next-Nearest-Neighbour Interaction
研究了具有铁磁次近邻（NNN）相互作用的自旋为1/2的铁磁-反铁磁交替海森堡链。基态是弱NNN相互作用的Halcite相，弱反铁磁相互作用的铁磁相。我们发现了一系列的拓扑结构不同的自旋间隙相位与各种幅度的边缘自旋强NNN相互作用。这些相位之间的相位边界是基于DMRG计算确定的，具有补偿边缘自旋的附加自旋。结果发现，在铁磁-铁磁相边界上具有短程反铁磁关联的精确解代表了每个自旋能隙相。
Boosting Nearest-Neighbour to Long-Range Integrable Spin Chains
我们提出了一个保积递推关系的显式构造的长程自旋链哈密顿量。这些链是Haldane-Shastry和Inozemtsev模型的推广，它们在弦/规范对偶性的最新进展中发挥了重要作用。该方法是基于任意近邻可积自旋链，它揭示了变形参数的模空间。我们还导出了闭链渐近Bethe方程。
Ising models with frustrated next-nearest-neighbor interactions present a rich morphology of modulated phases. These phases, however, assemble and relax slowly, which hinders their computational study. In two dimensions, strong fluctuations further hamper determining their equilibrium phase behavior from theoretical approximations. The exact numerical transfer matrix (TM) method, which bypasses these difficulties, can serve as a benchmark method once its own numerical challenges are surmounted. Building on our recent study [Hu and Charbonneau, Phys. Rev. B 103, 094441 (2021)], in which we eval…
A Monte Carlo Approach for Studying Microphases Applied to the Axial Next-Nearest-Neighbor Ising and the Ising-Coulomb Models
众所周知，微相形成系统的平衡相行为很难获得，因为它们的调制相的扩展亚稳性。在本文中，我们提出了一个系统的模拟方法，研究层状微相和应用的方法，两个原型的晶格为基础的系统：三维轴向次近邻伊辛（ANNNI）和伊辛库仑（IC）模型。该方法涉及沿着在有序场下的自由自旋的参考系和感兴趣的系统之间建立的可逆路径进行积分。由此产生的自由能计算明确地定位相边界。简单的阶段没有观察到发挥特别重要的作用，在魔鬼的花朵。利用广义序参量，研究了ANNNI模型的顺磁调制临界跃迁。我们证实了XY的顺磁调制过渡的普遍性和各向同性的性质。发现界面粗糙化在ANNNI层状制度中至多起很小的作用。
The paper is concerned with interacting particle systems on the simple cubic lattice obeying the nearest neighbour exclusion (NNE). This constraint forbids any two neighbouring sites of the lattice to be simultaneously occupied, thus reducing the set of admissible configurations for the cubic cell and its subclusters such as edges and faces. This reduction extends applicability of Kikuchi's Cluster Variation Method (CVM) with higher-order clusters to systems with complex site configurations and short-range ordering, which would be impractical beyond the NNE framework because of the "curse of d…
Crossovers in the Two Dimensional Ising Spin Glass with ferromagnetic next-nearest-neighbor interactions
通过大量的计算机模拟，我们详细分析了具有铁磁次近邻相互作用的二维$\pm J$伊辛自旋玻璃。我们发现了一个交叉从铁磁到"自旋玻璃“一样的顺序从数值模拟和分析参数。我们还提出了第二个交叉的证据，从“自旋玻璃”的行为的顺磁相的最大体积的研究。
Exact solution for a general FJC polyelectrolyte model with up to Next Nearest Neighbour Interactions
本文针对可电离珠子、刚性键且含至次近邻德拜-休克尔静电作用的自由连接链聚电解质模型，用转移矩阵法求得构象与质子化性质的精确解，并揭示有限链端基效应及向无限链极限的快速收敛。
Monte Carlo Study of the Axial Next-Nearest-Neighbor Ising Model
众所周知，由于调制相的扩展亚稳性，微相形成物质和模型的平衡相行为很难获得。我们开发了一种基于热力学积分的模拟方法，避免了这个问题，并与我们获得的典型的三维轴向次近邻伊辛模型的相图。平衡魔鬼的楼梯，磁化强度和磁化率。临界指数证实了超过Lifshitz点的无序调制相变的XY性质。结果确定用于分析这个基本的微相形成模型的各种近似方案的局限性。
We study Ising pyrochlores by means of Monte Carlo simulations. We cover a set of exchange constants ranging from the frustrated ferromagnetic case (spin-ice) to the fully-ordered "all-in--all-out" antiferromagnet in the dipolar model, reinterpreting the results --as in an ionic system-- in terms of a temperature vs. magnetic charge density phase diagram. In spite of its spin nature and the presence of both double and single non-conserved magnetic charges, the dipolar model gives place to a phase diagram which is quite comparable with those previously obtained for on-lattice systems of electri…
Wang-Landau study of the random bond square Ising model with nearest- and next-nearest-neighbor interactions
本文报道了具有最近邻（$J_{nn}$）和次最近邻（$J_{nnn}$）反铁磁相互作用的无规键方伊辛模型的Wang-Landau研究结果。我们考虑的情况下，$R=J_{nn}/J_{nnn}=1$的相互作用的竞争性质产生的亚晶格有序被称为超反铁磁性和纯系统经历了一个二阶过渡与一个积极的比热指数$α$。对于一个特定的无序强度，我们研究了键的随机性的影响，我们发现，而相关长度$ν$，磁化$β$，和磁化率$γ$的临界指数增加时相比，纯模型，比例$β/ν$和$γ/ν$保持不变。因此，无序系统服从弱普适性和超标度类似于其他二维无序系统。然而，比热表现出异常强的饱和行为，区分竞争相互作用的其他二维随机键系统以前研究的本案例。
Self-avoiding trails with nearest neighbour interactions on the square lattice
稀溶液中聚合物线圈的两种模型，自避行走和自避轨迹，已被证明是由相同的普适类。另一方面，通过最近邻接触相互作用的自回避行走（ISAW）和通过多次访问的网站相互作用的自回避轨迹（ISAT）是两种模型的线圈球，或崩溃过渡的聚合物在稀溶液中。在正方形格子上，数值计算表明，每个模型的坍缩跃迁属于不同的普适类。这些模型在两个实质性方面有所不同。它们的不同之处在于所使用的随机游走配置的子集的类型（网站自我回避与债券自我回避）和有吸引力的相互作用的类型。因此，考虑通过最近邻吸引力（INNSAT）相互作用的自回避轨迹，以确定崩溃普适性类差异的来源，是有一定意义的。使用flatPERM算法，我们已经进行了计算机模拟这个模型。我们提出的数值证据表明，INNSAT的自由能在崩溃过渡的奇异性有一个类似的指数的ISAW模型，而不是ISAT模型。这将表明，在ISAW和ISAT中使用的交互作用类型是普适性类差异的来源。
We classify all regular solutions of the Yang-Baxter equation of eight-vertex type. Regular solutions correspond to spin chains with nearest-neighbour interactions. We find a total of four independent solutions. Two are related to the usual six- and eight-vertex models that have R-matrices of difference form. We find two completely new solutions of the Yang-Baxter equation, which are manifestly of non-difference form. These new solutions contain the S-matrices of the AdS2 and AdS3 integrable models as a special case. Consequently, we can classify all possible integrable deformations of eight-v…
Simple cubic random-site percolation thresholds for complex neighbourhoods
在这种通信与计算机模拟，我们评估简单的三次随机网站渗透阈值的邻域，包括最近的邻居（NN），下一个最近的邻居（2NN）和下一个下一个最近的邻居（3 NN）。我们的估计是基于有限尺寸标度分析的渗透概率与网站占用概率图。Hoshen-Kopelman算法已被应用于集群标签。对于（NN + 2NN）、（NN +3 NN）、（NN + 2NN +3 NN）、2NN、（2NN +3 NN）、3 NN邻域，计算出的阈值分别为0.1372（1）、0.1420（1）、0.0976（1）、0.1991（1）、0.1036（1）、0.2455（1）。在一个正方形的晶格所获得的结果相比，计算出的逾渗阈值单调减少与网站的协调数z，至少对于我们检查的邻域。
The exact susceptibility of the spin-S transverse Ising chain with next-nearest-neighbor interactions
针对含次近邻相互作用的自旋-S横场Ising链，本文精确求解零场磁化率，给出S=1/2显式结果及一般S的转移矩阵表达，并揭示低温极限与S无关且在相变点发散。
Quasispins of vacancy defects in Ising chains with nearest- and next-to-nearest-neighbour interactions
本文研究具有最近邻和次近邻相互作用的一维伊辛链中空位缺陷的磁性质，提出空位可产生准自旋贡献并改变有效链长，揭示了不同短程序下准自旋效应的主导条件。
We classify all fundamental integrable spin chains with two-dimensional local Hilbert space which have regular R-matrices of difference form. This means that the R-matrix underlying the integrable structures is of the form R(u,v)=R(u-v) and reduces to the permutation operator at some particular point. We find a total of 14 independent solutions, 8 of which correspond to well-known eight or lower vertex models. The remaining 6 models appear to be new and some have peculiar properties such as not being diagonalizable or being nilpotent. Furthermore, for even R-matrices, we find a bijection betwe…
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