The Néel temperature, TN, of quasi-one-and quasi-two-dimensional antiferromagnetic Heisenberg models on a cubic lattice is calculated by Monte Carlo simulations as a function of inter-chain (interlayer) to intra-chain (intra-layer) coupling J ′ /J down to J ′ /J ≃ 10 −3 . We find that TN obeys a modified random-phase approximation-like relation for small J ′ /J with an effective universal renormalized coordination number, independent of the size of the spin. Empirical formulae describing TN for a wide range of J ′ and useful for the analysis of experimental measurements are presented.While genuinely one-dimensional (1D) and two-dimensional (2D) antiferromagnetic Heisenberg (AFH) models cannot display long-range order (LRO) except at zero temperature [1], weak inter-chain or inter-layer couplings, J ′ , which always exist in real materials, lead to a finite Néel temperature T N . So far, the J ′ -dependence of T N was calculated by exactly treating effects of the strong interaction J in the 1D or 2D system, but using mean-field approximations for the inter-chain and interlayer coupling. Recently, more advanced theories of the latter effects have been proposed for quasi-1D (Q1D) [3,4] and quasi-2D (Q2D) [5] systems, and the results have been compared with the experimental observations on Q1D antiferromagnets, e.g., Sr 2 CuO 3 [6], and Q2D antiferromagnets, e.g., La 2 CuO 4 [7]. In view of the importance of experimentally well-studied Q2D antiferromagnets as undoped parent compounds of the high-temperature superconductors, accurate and unbiased numerical results for Q1D and Q2D AFH models are strongly desired. In a recent work along this line, Sengupta et al. [8] have demonstrated peculiar temperature dependences of the specific heat in the quantum Q2D AFH model.Here we calculate the Néel temperature T N as a function of J ′ in fully three-dimensional (3D) classical and quantum Monte Carlo (MC) simulations of coupledchains and coupled-layers. Our MC results on the quantum spin-S and classical S = ∞ AFH models are analyzed by a modified random-phase approximation (RPA) with a renormalized coordination number defined bywhere χ s (T ) is the staggered susceptibility of the 1D or 2D model at temperature T . In a simple RPA calculation [2], this quantity is just the coordination number z d in the inter-chain or inter-layer directions: z 1 = 4 and z 2 = 2 for the Q1D and Q2D systems, respectively. Our main result is that ζ(J ′ ) evaluated by Eq. (1) with our numerically obtained T N (J ′ ) and χ s (T ) becomes constant, with the constants k 1 = 0.695 and k 2 = 0.65. These constants k d differ from the simple RPA result k d = 1, but the value of k 1 is consistent with the modified self-consistent RPA theory for the quantum Q1D (q-Q1D) model of Irkhin and Katanin (IK) [3]. Furthermore we find, that, within our numerical accuracy, the value of k d is the same for the S = 1/2, S = 1, S = 3/2 and S = ∞, and we conjecture that k d is universal and independent of the spin S for small J ′ /J. We also propose empirical formulae ...

No abstract

Emotional exhaustion (EE) is the core component in the study of teacher burnout, with significant impact on teachers’ professional lives. Yet, its relation to teachers’ emotional experiences and emotional labor (EL) during instruction remains unclear. Thirty-nine German secondary teachers were surveyed about their EE (trait), and via the experience sampling method on their momentary (state; N = 794) emotional experiences (enjoyment, anxiety, anger) and momentary EL (suppression, faking). Teachers reported that in 99 and 39% of all lessons, they experienced enjoyment and anger, respectively, whereas they experienced anxiety less frequently. Teachers reported suppressing or faking their emotions during roughly a third of all lessons. Furthermore, EE was reflected in teachers’ decreased experiences of enjoyment and increased experiences of anger. On an intra-individual level, all three emotions predict EL, whereas on an inter-individual level, only anger evokes EL. Explained variances in EL (within: 39%, between: 67%) stress the relevance of emotions in teaching and within the context of teacher burnout. Beyond implying the importance of reducing anger, our findings suggest the potential of enjoyment lessening EL and thereby reducing teacher burnout.

This paper examines students' achievement and interest and the extent to which they are predicted by teacher knowledge and motivation. Student achievement and interest are both considered desirable outcomes of school instruction. Teacher pedagogical content knowledge has been identified a major predictor of student achievement in previous research, whereas teacher motivation is considered a decisive factor influencing students' interest. So far, however, most research either focused on knowledge or motivation (both on the students' as well as the teachers' side), rarely investigating them together or examining the instructional mechanisms through which the supposed effects of teacher knowledge and motivation are facilitated. In the present study, N ¼ 77 physics teachers and their classes in Germany and Switzerland are investigated utilizing a multi-method approach in combining data obtained from testinstruments (teacher pedagogical content knowledge, student achievement) and questionnaires (teacher motivation, student interest, student perceived enthusiastic teaching) as well as videotaped instruction (cognitive activation rated by observers). Multi-level structural equation modeling was used to support the assumptions that teacher pedagogical content knowledge positively predicted students' achievement; the effect was mediated by cognitive activation. Teachers' motivation predicted students' interest which was mediated by enthusiastic teaching as perceived by students. Neither did teacher pedagogical content knowledge predict students' interest, nor teacher motivation students' achievement. This implies that in order to improve students' cognitive as well as affective outcomes, both teachers' knowledge but also their motivation need to be considered. motivation need to be considered.

Although teacher enthusiasm is a relevant variable in the teaching context, a clear definition is still lacking. Research on teacher enthusiasm is characterized by ambiguous conceptualizations of enthu siasm as either an affective characteristic of teachers or behaviors of expressiveness. Integrating these two notions, a new conceptualization of dispositional teacher enthusiasm, defined by teachers' positive affect and positive emotional expressivity, was developed. It was hypothesized that dispositional teacher enthusiasm would relate to students' interest, mediated by students' perceived teacher enthusiasm. Based on a correlational study design, secondary teachers (N ¼ 75) from Switzerland reported on their enthusiasm, complemented by student ratings (N ¼ 1523) on perceived enthusiasm and interest. Multilevel structural equation modeling revealed that dispositional teacher enthusiasm positively pre dicted students' interest, which was fully mediated by students' perceived enthusiasm, providing the basis of a valid definition of teacher enthusiasm. Based on this integrative definition, implications for future research are discussed.

a b s t r a c tThis study investigated the relations between eight characteristics of teaching and students' academic emotions (enjoyment, pride, anxiety, anger, helplessness and boredom) across four academic domains (mathematics, physics, German, and English). 121 students (50% female; 8th and 11th graders) were asked about their perceptions of teaching characteristics and their academic emotions using the experience sampling method (real-time approach) for a period of 10 school days, with intraindividual analyses conducted using a multilevel approach. Multilevel exploratory factor analysis revealed that the eight teaching characteristics (understandability, illustration, enthusiasm, fostering attention, lack of clarity, difficulty, pace, level of expectation) represented two factors, labeled supportive presentation style (e.g., comprising understandability) and excessive lesson demands (e.g., comprising difficulty). In line with our hypothesis, we found clear relations on the intraindividual level between the two factors of teaching characteristics and students' academic emotions in the classroom (e.g., supportive presentation style positively related to students' enjoyment and negatively related to their boredom). Further, and supporting the universality assumption of teaching characteristics/academic emotions relations, the strength of relations between the two factors of teaching characteristics and academic emotions was very similar across the four academic domains. Implications for future research and educational practice are discussed.

No abstract

Using a preexisting, but as yet empirically untested theoretical model, the present study investigated antecedents of teachers’ emotions in the classroom. More specifically, the relationships between students’ motivation and discipline and teachers’ enjoyment and anger were explored, as well as if these relationships are mediated by teachers’ subjective appraisals (goal conduciveness and coping potential). The study employed an intraindividual approach by collecting data through a diary. The sample consisted of 39 teachers who each participated with one of their 9th or 10th grade mathematics classes (N = 758 students). Both teachers and students filled out diaries for 2–3 weeks pertaining to 8.10 lessons on average (N = 316 lessons). Multilevel structural equation modeling revealed that students’ motivation and discipline explained 24% of variance in teachers’ enjoyment and 26% of variance in teachers’ anger. In line with theoretical assumptions, after introducing teachers’ subjective appraisals as a mediating mechanism into the model, the explained variance systematically increased to 65 and 61%, for teachers’ enjoyment and anger respectively. The effects of students’ motivation and discipline level on teachers’ emotions were partially mediated by teachers’ appraisals of goal conduciveness and coping potential. The findings imply that since teachers’ emotions depend to a large extent on subjective evaluations of a situation, teachers should be able to directly modify their emotional experiences during a lesson through cognitive reappraisals.